Lecture notes on regularity theory for the Navier-Stokes equations /:
The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes eq...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey :
World Scientific,
[2014]
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789814623414 9814623415 |
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| 245 | 1 | 0 | |a Lecture notes on regularity theory for the Navier-Stokes equations / |c Gregory Seregin. |
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions. | |
| 505 | 8 | |a 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions. | |
| 505 | 8 | |6 880-01 |a Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index. | |
| 520 | |a The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value. | ||
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| 650 | 2 | |a Hydrodynamics |0 https://id.nlm.nih.gov/mesh/D057446 | |
| 650 | 6 | |a Équations de Navier-Stokes. | |
| 650 | 6 | |a Dynamique des fluides. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
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| contents | Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions. 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions. Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index. |
| ctrlnum | (OCoLC)894894804 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Seregin, Gregory, 1950- author. https://id.oclc.org/worldcat/entity/E39PCjJg4kktb9yFfWvhvh7d8K http://id.loc.gov/authorities/names/n00008872 Lecture notes. Selections Lecture notes on regularity theory for the Navier-Stokes equations / Gregory Seregin. New Jersey : World Scientific, [2014] ©2015 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. Includes bibliographical references and index. Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions. 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions. 880-01 Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index. The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value. Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Équations de Navier-Stokes. Dynamique des fluides. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fluid dynamics fast Navier-Stokes equations fast has work: Selections Lecture notes (Text) https://id.oclc.org/worldcat/entity/E39PCG3h36FDHrW7PQpGWk6f9C https://id.oclc.org/worldcat/ontology/hasWork Print version: Seregin, Gregory, 1950- Lecture notes. Selections. Lecture notes on regularity theory for the Navier-Stokes equations 9789814623407 (DLC) 2014024553 (OCoLC)881721527 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886709 Volltext 505-01/(S 5.7 Strong Solutions5.8 Comments; 6. Local Regularity Theory for Non-Stationary Navier-Stokes Equations; 6.1 ε-Regularity Theory; 6.2 Bounded Ancient Solutions; 6.3 Mild Bounded Ancient Solutions; 6.4 Liouville Type Theorems; 6.4.1 LPS Quantities; 6.4.2 2D case; 6.4.3 Axially Symmetric Case with No Swirl; 6.4.4 Axially Symmetric Case; 6.5 Axially Symmetric Suitable Weak Solutions; 6.6 Backward Uniqueness for Navier-Stokes Equations; 6.7 Comments; 7. Behavior of L3-Norm; 7.1 Main Result; 7.2 Estimates of Scaled Solutions; 7.3 Limiting Procedure; 7.4 Comments. |
| spellingShingle | Seregin, Gregory, 1950- Lecture notes on regularity theory for the Navier-Stokes equations / Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions. 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions. Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index. Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Équations de Navier-Stokes. Dynamique des fluides. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fluid dynamics fast Navier-Stokes equations fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85090420 http://id.loc.gov/authorities/subjects/sh85049376 https://id.nlm.nih.gov/mesh/D057446 |
| title | Lecture notes on regularity theory for the Navier-Stokes equations / |
| title_alt | Lecture notes. |
| title_auth | Lecture notes on regularity theory for the Navier-Stokes equations / |
| title_exact_search | Lecture notes on regularity theory for the Navier-Stokes equations / |
| title_full | Lecture notes on regularity theory for the Navier-Stokes equations / Gregory Seregin. |
| title_fullStr | Lecture notes on regularity theory for the Navier-Stokes equations / Gregory Seregin. |
| title_full_unstemmed | Lecture notes on regularity theory for the Navier-Stokes equations / Gregory Seregin. |
| title_short | Lecture notes on regularity theory for the Navier-Stokes equations / |
| title_sort | lecture notes on regularity theory for the navier stokes equations |
| topic | Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Fluid dynamics. http://id.loc.gov/authorities/subjects/sh85049376 Hydrodynamics https://id.nlm.nih.gov/mesh/D057446 Équations de Navier-Stokes. Dynamique des fluides. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fluid dynamics fast Navier-Stokes equations fast |
| topic_facet | Navier-Stokes equations. Fluid dynamics. Hydrodynamics Équations de Navier-Stokes. Dynamique des fluides. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Fluid dynamics Navier-Stokes equations |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886709 |
| work_keys_str_mv | AT seregingregory lecturenotes AT seregingregory lecturenotesonregularitytheoryforthenavierstokesequations |