Introduction to the mathematical theory of compressible flow /:
This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;Th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford ; New York :
Oxford University Press,
2004.
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications ;
27. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to. |
| Beschreibung: | 1 online resource (xx, 506 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780191523953 019152395X 1280845228 9781280845222 |
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| 245 | 1 | 0 | |a Introduction to the mathematical theory of compressible flow / |c A. Novotný, I. Straéskraba. |
| 260 | |a Oxford ; |a New York : |b Oxford University Press, |c 2004. | ||
| 300 | |a 1 online resource (xx, 506 pages) | ||
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| 490 | 1 | |a Oxford lecture series in mathematics and its applications ; |v 27 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to. | ||
| 505 | 0 | |a 1 Fundamental concepts and equations -- 1.1 Some mathematical concepts and notation -- 1.1.1 Basic notation -- 1.1.2 Some useful inequalities in IR[sup(N)] -- 1.1.3 Differential operators -- 1.1.4 Gronwall's lemma -- 1.1.5 Implicit functions -- 1.1.6 Transformations of Cartesian coordinates -- 1.1.7 Hölder-continuous and Lipschitz functions -- 1.1.8 The symbols "o" and "O" -- 1.1.9 Partitions of unity -- 1.1.10 Measure -- 1.1.11 Description of the boundary -- 1.1.12 Measure on the boundary of a domain -- 1.1.13 Classical Green's theorem -- 1.1.14 Lebesgue spaces. | |
| 505 | 8 | |a 1.1.15 Lebesgue's points -- 1.1.16 Absolutely continuous functions -- 1.1.17 Absolute continuity of integrals with respect to measurable subsets -- 1.1.18 Some theorems from integration theory -- 1.2 Governing equations and relations of gas dynamics -- 1.2.1 Description of the flow -- 1.2.2 The transport theorem -- 1.2.3 The continuity equation -- 1.2.4 The equations of motion -- 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor -- 1.2.6 Inviscid and viscous fluids -- 1.2.7 The energy equation -- 1.2.8 The second law of thermodynamics and the entropy. | |
| 505 | 8 | |a 1.2.9 Principle of material frame indifference -- 1.2.10 Newtonian fluids -- 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids -- 1.2.12 Entropy form of the energy equation for Newtonian fluids -- 1.2.13 Some consequences of the Clausius-Duhem inequality -- 1.2.14 Equations of state -- 1.2.15 Adiabatic flow of a perfect inviscid gas -- 1.2.16 Compressible Euler equations -- 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas -- 1.2.18 Barotropic flow of a viscous gas -- 1.2.19 Speed of sound -- 1.2.20 Simplified models. | |
| 505 | 8 | |a 1.2.21 Initial and boundary conditions -- 1.3 Some advanced mathematical concepts and results -- 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](])* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results. | |
| 505 | 8 | |a 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation. | |
| 546 | |a English. | ||
| 650 | 0 | |a Fluid dynamics |x Mathematical models. | |
| 650 | 0 | |a Compressibility. |0 http://id.loc.gov/authorities/subjects/sh85029439 | |
| 650 | 6 | |a Dynamique des fluides |x Modèles mathématiques. | |
| 650 | 6 | |a Compressibilité. | |
| 650 | 7 | |a compressibility. |2 aat | |
| 650 | 7 | |a compression. |2 aat | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Material Science. |2 bisacsh | |
| 650 | 7 | |a Compressibility |2 fast | |
| 650 | 7 | |a Fluid dynamics |x Mathematical models |2 fast | |
| 700 | 1 | |a Straéskraba, I. |q (Ivan) | |
| 758 | |i has work: |a Introduction to the mathematical theory of compressible flow (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGpWDYQxTGCb9WHv8Y4jG3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Novotný, A. |t Introduction to the mathematical theory of compressible flow. |d Oxford ; New York : Oxford University Press, 2004 |w (DLC) 2004301771 |
| 830 | 0 | |a Oxford lecture series in mathematics and its applications ; |v 27. |0 http://id.loc.gov/authorities/names/n94044383 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=264886 |3 Volltext |
| 880 | 8 | |6 505-00/(S |a 2.2.15 Quasilinear system -- 2.2.16 Local existence for a quasilinear system -- 2.2.17 Second grade approximations -- 2.2.18 Higher order energy estimates -- 2.2.19 Convergence of approximations -- 2.2.20 Uniqueness -- 2.2.21 Local existence for equations of an isentropic ideal gas -- 2.2.22 Existence of global smooth solutions for nonlinear hyperbolic systems -- 2.2.23 2 × 2 system of conservation laws, Riemann invariants -- 2.2.24 Plane wave solutions -- 2.2.25 Plane waves for the Euler system in 2D -- 2.3 Weak solutions -- 2.3.1 Blow up of classical solutions -- 2.3.2 Generalized formulation for systems of conservation laws -- 2.3.3 Piecewise smooth solutions -- 2.3.4 Entropy condition -- 2.3.5 Physical entropy -- 2.3.6 General parabolic approximation and the entropy condition -- 2.3.7 Entropy for a general scalar conservation law -- 2.3.8 Entropy for a 2 × 2 system of conservation laws in 1D -- 2.3.9 Entropy function for a p-system -- 2.3.10 Riemann problem -- 2.3.11 Riemann problem for 2 × 2 isentropic gas dynamics equations -- 2.3.12 Existence and uniqueness of admissible weak solution for a scalar conservation law -- 2.3.13 Plane waves admitting discontinuities -- 2.3.14 Existence of solutions to the 2 × 2 Euler system for an isentropic gas -- 2.3.15 Lax-Friedrichs difference approximations -- 2.3.16 Existence of approximations -- 2.3.17 Invariant regions for Riemann invariants -- 2.3.18 Compactness argument -- 2.3.19 Characterization of the weak limit by Young measure -- 2.3.20 Div-curl lemma and Tartar's commutation relation -- 2.3.21 Existence of weak entropy-entropy flux pairs -- 2.3.22 Localization of supp ν -- 2.3.23 Approximative limit is an admissible solution -- 2.3.24 Global existence for general systems in one dimension -- 2.4 Final comments -- 2.4.1 Local existence results -- 2.4.2 Global smooth solutions. | |
| 880 | 8 | |6 505-00/(S |a 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](Ω)* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results -- 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation -- 2.1.2 One-dimensional Euler equations -- 2.1.3 Lagrangian mass coordinates -- 2.1.4 Symmetrizable systems -- 2.1.5 Matrix form of the p-system -- 2.1.6 The Euler equations of an inviscid gas -- 2.2 Existence of smooth solutions -- 2.2.1 Hyperbolic systems and characteristics -- 2.2.2 Cauchy problem for system of conservation laws -- 2.2.3 Linear scalar equation -- 2.2.4 Solution of a linear system -- 2.2.5 Nonlinear scalar equation -- 2.2.6 Piston problem -- 2.2.7 Complementary Riemann invariants -- 2.2.8 Solution of the piston problem -- 2.2.9 Cauchy problem for a symmetric hyperbolic system -- 2.2.10 Approximations -- 2.2.11 Existence of approximations -- 2.2.12 Energy estimate -- 2.2.13 Convergence of approximations to a generalized solution -- 2.2.14 Regularity of the generalized solution. | |
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| author | Novotný, A. |
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| contents | 1 Fundamental concepts and equations -- 1.1 Some mathematical concepts and notation -- 1.1.1 Basic notation -- 1.1.2 Some useful inequalities in IR[sup(N)] -- 1.1.3 Differential operators -- 1.1.4 Gronwall's lemma -- 1.1.5 Implicit functions -- 1.1.6 Transformations of Cartesian coordinates -- 1.1.7 Hölder-continuous and Lipschitz functions -- 1.1.8 The symbols "o" and "O" -- 1.1.9 Partitions of unity -- 1.1.10 Measure -- 1.1.11 Description of the boundary -- 1.1.12 Measure on the boundary of a domain -- 1.1.13 Classical Green's theorem -- 1.1.14 Lebesgue spaces. 1.1.15 Lebesgue's points -- 1.1.16 Absolutely continuous functions -- 1.1.17 Absolute continuity of integrals with respect to measurable subsets -- 1.1.18 Some theorems from integration theory -- 1.2 Governing equations and relations of gas dynamics -- 1.2.1 Description of the flow -- 1.2.2 The transport theorem -- 1.2.3 The continuity equation -- 1.2.4 The equations of motion -- 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor -- 1.2.6 Inviscid and viscous fluids -- 1.2.7 The energy equation -- 1.2.8 The second law of thermodynamics and the entropy. 1.2.9 Principle of material frame indifference -- 1.2.10 Newtonian fluids -- 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids -- 1.2.12 Entropy form of the energy equation for Newtonian fluids -- 1.2.13 Some consequences of the Clausius-Duhem inequality -- 1.2.14 Equations of state -- 1.2.15 Adiabatic flow of a perfect inviscid gas -- 1.2.16 Compressible Euler equations -- 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas -- 1.2.18 Barotropic flow of a viscous gas -- 1.2.19 Speed of sound -- 1.2.20 Simplified models. 1.2.21 Initial and boundary conditions -- 1.3 Some advanced mathematical concepts and results -- 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](])* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results. 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation. |
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| id | ZDB-4-EBA-ocn314216971 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780191523953 019152395X 1280845228 9781280845222 |
| language | English |
| oclc_num | 314216971 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xx, 506 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Oxford University Press, |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications ; |
| series2 | Oxford lecture series in mathematics and its applications ; |
| spelling | Novotný, A. http://id.loc.gov/authorities/names/nb2004302471 Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba. Oxford ; New York : Oxford University Press, 2004. 1 online resource (xx, 506 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Oxford lecture series in mathematics and its applications ; 27 Includes bibliographical references and index. Print version record. This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to. 1 Fundamental concepts and equations -- 1.1 Some mathematical concepts and notation -- 1.1.1 Basic notation -- 1.1.2 Some useful inequalities in IR[sup(N)] -- 1.1.3 Differential operators -- 1.1.4 Gronwall's lemma -- 1.1.5 Implicit functions -- 1.1.6 Transformations of Cartesian coordinates -- 1.1.7 Hölder-continuous and Lipschitz functions -- 1.1.8 The symbols "o" and "O" -- 1.1.9 Partitions of unity -- 1.1.10 Measure -- 1.1.11 Description of the boundary -- 1.1.12 Measure on the boundary of a domain -- 1.1.13 Classical Green's theorem -- 1.1.14 Lebesgue spaces. 1.1.15 Lebesgue's points -- 1.1.16 Absolutely continuous functions -- 1.1.17 Absolute continuity of integrals with respect to measurable subsets -- 1.1.18 Some theorems from integration theory -- 1.2 Governing equations and relations of gas dynamics -- 1.2.1 Description of the flow -- 1.2.2 The transport theorem -- 1.2.3 The continuity equation -- 1.2.4 The equations of motion -- 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor -- 1.2.6 Inviscid and viscous fluids -- 1.2.7 The energy equation -- 1.2.8 The second law of thermodynamics and the entropy. 1.2.9 Principle of material frame indifference -- 1.2.10 Newtonian fluids -- 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids -- 1.2.12 Entropy form of the energy equation for Newtonian fluids -- 1.2.13 Some consequences of the Clausius-Duhem inequality -- 1.2.14 Equations of state -- 1.2.15 Adiabatic flow of a perfect inviscid gas -- 1.2.16 Compressible Euler equations -- 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas -- 1.2.18 Barotropic flow of a viscous gas -- 1.2.19 Speed of sound -- 1.2.20 Simplified models. 1.2.21 Initial and boundary conditions -- 1.3 Some advanced mathematical concepts and results -- 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](])* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results. 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation. English. Fluid dynamics Mathematical models. Compressibility. http://id.loc.gov/authorities/subjects/sh85029439 Dynamique des fluides Modèles mathématiques. Compressibilité. compressibility. aat compression. aat TECHNOLOGY & ENGINEERING Material Science. bisacsh Compressibility fast Fluid dynamics Mathematical models fast Straéskraba, I. (Ivan) has work: Introduction to the mathematical theory of compressible flow (Text) https://id.oclc.org/worldcat/entity/E39PCGpWDYQxTGCb9WHv8Y4jG3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Novotný, A. Introduction to the mathematical theory of compressible flow. Oxford ; New York : Oxford University Press, 2004 (DLC) 2004301771 Oxford lecture series in mathematics and its applications ; 27. http://id.loc.gov/authorities/names/n94044383 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=264886 Volltext 505-00/(S 2.2.15 Quasilinear system -- 2.2.16 Local existence for a quasilinear system -- 2.2.17 Second grade approximations -- 2.2.18 Higher order energy estimates -- 2.2.19 Convergence of approximations -- 2.2.20 Uniqueness -- 2.2.21 Local existence for equations of an isentropic ideal gas -- 2.2.22 Existence of global smooth solutions for nonlinear hyperbolic systems -- 2.2.23 2 × 2 system of conservation laws, Riemann invariants -- 2.2.24 Plane wave solutions -- 2.2.25 Plane waves for the Euler system in 2D -- 2.3 Weak solutions -- 2.3.1 Blow up of classical solutions -- 2.3.2 Generalized formulation for systems of conservation laws -- 2.3.3 Piecewise smooth solutions -- 2.3.4 Entropy condition -- 2.3.5 Physical entropy -- 2.3.6 General parabolic approximation and the entropy condition -- 2.3.7 Entropy for a general scalar conservation law -- 2.3.8 Entropy for a 2 × 2 system of conservation laws in 1D -- 2.3.9 Entropy function for a p-system -- 2.3.10 Riemann problem -- 2.3.11 Riemann problem for 2 × 2 isentropic gas dynamics equations -- 2.3.12 Existence and uniqueness of admissible weak solution for a scalar conservation law -- 2.3.13 Plane waves admitting discontinuities -- 2.3.14 Existence of solutions to the 2 × 2 Euler system for an isentropic gas -- 2.3.15 Lax-Friedrichs difference approximations -- 2.3.16 Existence of approximations -- 2.3.17 Invariant regions for Riemann invariants -- 2.3.18 Compactness argument -- 2.3.19 Characterization of the weak limit by Young measure -- 2.3.20 Div-curl lemma and Tartar's commutation relation -- 2.3.21 Existence of weak entropy-entropy flux pairs -- 2.3.22 Localization of supp ν -- 2.3.23 Approximative limit is an admissible solution -- 2.3.24 Global existence for general systems in one dimension -- 2.4 Final comments -- 2.4.1 Local existence results -- 2.4.2 Global smooth solutions. 505-00/(S 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](Ω)* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results -- 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation -- 2.1.2 One-dimensional Euler equations -- 2.1.3 Lagrangian mass coordinates -- 2.1.4 Symmetrizable systems -- 2.1.5 Matrix form of the p-system -- 2.1.6 The Euler equations of an inviscid gas -- 2.2 Existence of smooth solutions -- 2.2.1 Hyperbolic systems and characteristics -- 2.2.2 Cauchy problem for system of conservation laws -- 2.2.3 Linear scalar equation -- 2.2.4 Solution of a linear system -- 2.2.5 Nonlinear scalar equation -- 2.2.6 Piston problem -- 2.2.7 Complementary Riemann invariants -- 2.2.8 Solution of the piston problem -- 2.2.9 Cauchy problem for a symmetric hyperbolic system -- 2.2.10 Approximations -- 2.2.11 Existence of approximations -- 2.2.12 Energy estimate -- 2.2.13 Convergence of approximations to a generalized solution -- 2.2.14 Regularity of the generalized solution. |
| spellingShingle | Novotný, A. Introduction to the mathematical theory of compressible flow / Oxford lecture series in mathematics and its applications ; 1 Fundamental concepts and equations -- 1.1 Some mathematical concepts and notation -- 1.1.1 Basic notation -- 1.1.2 Some useful inequalities in IR[sup(N)] -- 1.1.3 Differential operators -- 1.1.4 Gronwall's lemma -- 1.1.5 Implicit functions -- 1.1.6 Transformations of Cartesian coordinates -- 1.1.7 Hölder-continuous and Lipschitz functions -- 1.1.8 The symbols "o" and "O" -- 1.1.9 Partitions of unity -- 1.1.10 Measure -- 1.1.11 Description of the boundary -- 1.1.12 Measure on the boundary of a domain -- 1.1.13 Classical Green's theorem -- 1.1.14 Lebesgue spaces. 1.1.15 Lebesgue's points -- 1.1.16 Absolutely continuous functions -- 1.1.17 Absolute continuity of integrals with respect to measurable subsets -- 1.1.18 Some theorems from integration theory -- 1.2 Governing equations and relations of gas dynamics -- 1.2.1 Description of the flow -- 1.2.2 The transport theorem -- 1.2.3 The continuity equation -- 1.2.4 The equations of motion -- 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor -- 1.2.6 Inviscid and viscous fluids -- 1.2.7 The energy equation -- 1.2.8 The second law of thermodynamics and the entropy. 1.2.9 Principle of material frame indifference -- 1.2.10 Newtonian fluids -- 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids -- 1.2.12 Entropy form of the energy equation for Newtonian fluids -- 1.2.13 Some consequences of the Clausius-Duhem inequality -- 1.2.14 Equations of state -- 1.2.15 Adiabatic flow of a perfect inviscid gas -- 1.2.16 Compressible Euler equations -- 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas -- 1.2.18 Barotropic flow of a viscous gas -- 1.2.19 Speed of sound -- 1.2.20 Simplified models. 1.2.21 Initial and boundary conditions -- 1.3 Some advanced mathematical concepts and results -- 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](])* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results. 1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation. Fluid dynamics Mathematical models. Compressibility. http://id.loc.gov/authorities/subjects/sh85029439 Dynamique des fluides Modèles mathématiques. Compressibilité. compressibility. aat compression. aat TECHNOLOGY & ENGINEERING Material Science. bisacsh Compressibility fast Fluid dynamics Mathematical models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85029439 |
| title | Introduction to the mathematical theory of compressible flow / |
| title_auth | Introduction to the mathematical theory of compressible flow / |
| title_exact_search | Introduction to the mathematical theory of compressible flow / |
| title_full | Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba. |
| title_fullStr | Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba. |
| title_full_unstemmed | Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba. |
| title_short | Introduction to the mathematical theory of compressible flow / |
| title_sort | introduction to the mathematical theory of compressible flow |
| topic | Fluid dynamics Mathematical models. Compressibility. http://id.loc.gov/authorities/subjects/sh85029439 Dynamique des fluides Modèles mathématiques. Compressibilité. compressibility. aat compression. aat TECHNOLOGY & ENGINEERING Material Science. bisacsh Compressibility fast Fluid dynamics Mathematical models fast |
| topic_facet | Fluid dynamics Mathematical models. Compressibility. Dynamique des fluides Modèles mathématiques. Compressibilité. compressibility. compression. TECHNOLOGY & ENGINEERING Material Science. Compressibility Fluid dynamics Mathematical models |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=264886 |
| work_keys_str_mv | AT novotnya introductiontothemathematicaltheoryofcompressibleflow AT straeskrabai introductiontothemathematicaltheoryofcompressibleflow |