Introduction to the mathematical theory of compressible flow:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2004
|
| Edition: | 1. publ. |
| Series: | Oxford lecture series in mathematics and its applications
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 506 S. |
| ISBN: | 0198530846 9780198530848 |
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| 100 | 1 | |a Novotný, Antonín |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to the mathematical theory of compressible flow |c A. Novotný ; I. Straškraba |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2004 | |
| 300 | |a XX, 506 S. | ||
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| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 27 | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Compressibility | |
| 650 | 4 | |a Fluid dynamics |x Mathematical models | |
| 650 | 0 | 7 | |a Kompressible Strömung |0 (DE-588)4032018-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mathematische Methode |0 (DE-588)4155620-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Straškraba, Ivan |e Verfasser |4 aut | |
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| adam_text | INTRODUCTION TO THE MATHEMATICAL THEORY OF COMPRESSIBLE FLOW A. NOVOTNY
UNIVERSITE DU SUD TOULON-VAR I. STRASKRABA MATHEMATICAL INSTITUTE OF THE
ACADEMY OF SCIENCES OF THE CZECH REPUBLIC OXFORD JNIVERSITY PRESS
CONTENTS FUNDAMENTAL CONCEPTS AND EQUATIONS 1 1.1 SOME MATHEMATICAL
CONCEPTS AND NOTATION 1 1.1.1 BASIC NOTATION 1 1.1.2 SOME USEFUL
INEQUALITIES IN M N 3 1.1.3 DIFFERENTIAL OPERATORS 3 1.1.4 GRONWALL S
LEMMA 5 1.1.5 IMPLICIT FUNCTIONS 5 1.1.6 TRANSFORMATIONS OF CARTESIAN
COORDINATES 6 1.1.7 HOLDER-CONTINUOUS AND LIPSCHITZ FUNCTIONS 6 1.1.8
THE SYMBOLS O AND O 7 1.1.9 PARTITIONS OF UNITY 7 1.1.10 MEASURE 7
1.1.11 DESCRIPTION OF THE BOUNDARY 8 1.1.12 MEASURE ON THE BOUNDARY OF A
DOMAIN 8 1.1.13 CLASSICAL GREEN S THEOREM 9 1.1.14 LEBESGUE SPACES 10
1.1.15 LEBESGUE S POINTS 11 1.1.16 ABSOLUTELY CONTINUOUS FUNCTIONS 12
1.1.17 ABSOLUTE CONTINUITY OF INTEGRALS WITH RESPECT TO MEASURABLE
SUBSETS 12 1.1.18 SOME THEOREMS FROM INTEGRATION THEORY 13 1.2 GOVERNING
EQUATIONS AND RELATIONS OF GAS DYNAMICS 15 1.2.1 DESCRIPTION OF THE FLOW
16 1.2.2 THE TRANSPORT THEOREM 17 1.2.3 THE CONTINUITY EQUATION 19 1.2.4
THE EQUATIONS OF MOTION 19 1.2.5 THE LAW OF CONSERVATION OF THE MOMENT
OF MOMENTUM. SYMMETRY OF THE STRESS TENSOR 21 1.2.6 INVISCID AND VISCOUS
FLUIDS 21 1.2.7 THE ENERGY EQUATION 22 1.2.8 THE SECOND LAW OF
THERMODYNAMICS AND THE ENTROPY 22 1.2.9 PRINCIPLE OF MATERIAL FRAME
INDIFFERENCE 23 1.2.10 NEWTONIAN FLUIDS 24 1.2.11 CONSERVATIVE AND
DISSIPATION FORM OF THE ENERGY EQUATION FOR NEWTONIAN FLUIDS 24 1.2.12
ENTROPY FORM OF THE ENERGY EQUATION FOR NEWTONIAN FLUIDS 25 CONTENTS
1.2.13 SOME CONSEQUENCES OF THE CLAUSIUS-DUHEM INEQUALITY 25 1.2.14
EQUATIONS OF STATE 26 1.2.15 ADIABATIC FLOW OF A PERFECT INVISCID GAS 27
1.2.16 COMPRESSIBLE EULER EQUATIONS 28 1.2.17 COMPRESSIBLE NAVIER-STOKES
EQUATIONS FOR A PERFECT VISCOUS GAS 28 1.2.18 BAROTROPIC FLOW OF A
VISCOUS GAS 29 1.2.19 SPEED OF SOUND 30 1.2.20 SIMPLIFIED MODELS 30
1.2.21 INITIAL AND BOUNDARY CONDITIONS 31 1.3 SOME ADVANCED MATHEMATICAL
CONCEPTS AND RESULTS 32 1.3.1 SPACES OF HOLDER-CONTINUOUS AND
CONTINUOUSLY DIFFERENTIABLE FUNCTIONS 33 1.3.2 YOUNG S FUNCTIONS,
JENSEN S INEQUALITY 33 1.3.3 ORLICZ SPACES 34 1.3.4 DISTRIBUTIONS 35
1.3.5 SOBOLEV SPACES 40 1.3.6 HOMOGENEOUS SOBOLEV SPACES 47 1.3.7
TEMPERED DISTRIBUTIONS 50 1.3.8 RADON MEASURE AND REPRESENTATION OF
CB(O)* 52 1.3.9 FUNCTIONS OF BOUNDED VARIATION 52 1.3.10 FUNCTIONS WITH
VALUES IN BANACH SPACES 53 1.3.11 SOBOLEV IMBEDDINGS OF ABSTRACT SPACES
57 1.3.12 SOME COMPACTNESS RESULTS 58 1.4 SURVEY OF CONCEPTS AND RESULTS
FROM FUNCTIONAL ANALYSIS 60 1.4.1 LINEAR VECTOR SPACES 60 1.4.2
TOPOLOGICAL LINEAR SPACES 60 1.4.3 METRIC LINEAR SPACE 62 1.4.4 NORMED
LINEAR SPACE 62 1.4.5 DUALS TO BANACH SPACES AND WEAK(-*) TOPOLOGIES 64
1.4.6 RIESZ REPRESENTATION THEOREM 68 1.4.7 OPERATORS 68 1.4.8 ELEMENTS
OF SPECTRAL THEORY 70 1.4.9 LAX-MILGRAM LEMMA 70 1.4.10 IMBEDDINGS 71
1.4.11 SOLUTION OF NONLINEAR OPERATOR EQUATIONS 71 THEORETICAL RESULTS
FOR THE EULER EQUATIONS 74 2.1 HYPERBOLIC SYSTEMS AND THE EULER
EQUATIONS 74 2.1.1 ZERO-VISCOSITY BURGERS EQUATION 75 2.1.2
ONE-DIMENSIONAL EULER EQUATIONS 76 2.1.3 LAGRANGIAN MASS COORDINATES 76
2.1.4 SYMMETRIZABLE SYSTEMS 77 CONTENTS XIII 2.1.5 MATRIX FORM OF THE
P-SYSTEM 77 2.1.6 THE EULER EQUATIONS OF AN INVISCID GAS 78 2.2
EXISTENCE OF SMOOTH SOLUTIONS 79 2.2.1 HYPERBOLIC SYSTEMS AND
CHARACTERISTICS 79 2.2.2 CAUCHY PROBLEM FOR SYSTEM OF CONSERVATION LAWS
80 2.2.3 LINEAR SCALAR EQUATION 81 2.2.4 SOLUTION OF A LINEAR SYSTEM 82
2.2.5 NONLINEAR SCALAR EQUATION 82 2.2.6 PISTON PROBLEM 84 2.2.7
COMPLEMENTARY RIEMANN INVARIANTS 84 2.2.8 SOLUTION OF THE PISTON PROBLEM
85 2.2.9 CAUCHY PROBLEM FOR A SYMMETRIC HYPERBOLIC SYSTEM 89 2.2.10
APPROXIMATIONS 90 2.2.11 EXISTENCE OF APPROXIMATIONS 90 2.2.12 ENERGY
ESTIMATE 91 2.2.13 CONVERGENCE OF APPROXIMATIONS TO A GENERALIZED
SOLUTION 92 2.2.14 REGULARITY OF THE GENERALIZED SOLUTION 92 2.2.15
QUASILINEAR SYSTEM 94 2.2.16 LOCAL EXISTENCE FOR A QUASILINEAR SYSTEM 95
2.2.17 SECOND GRADE APPROXIMATIONS 95 2.2.18 HIGHER ORDER ENERGY
ESTIMATES 95 2.2.19 CONVERGENCE OF APPROXIMATIONS 97 2.2.20 UNIQUENESS
98 2.2.21 LOCAL EXISTENCE FOR EQUATIONS OF AN ISENTROPIC IDEAL GAS 99
2.2.22 EXISTENCE OF GLOBAL SMOOTH SOLUTIONS FOR NONLINEAR HYPERBOLIC
SYSTEMS 100 2.2.23 2X2 SYSTEM OF CONSERVATION LAWS, RIEMANN INVARIANTS
100 2.2.24 PLANE WAVE SOLUTIONS 103 2.2.25 PLANE WAVES FOR THE EULER
SYSTEM IN ID 104 2.3 WEAK SOLUTIONS 106 2.3.1 BLOW UP OF CLASSICAL
SOLUTIONS 107 2.3.2 GENERALIZED FORMULATION FOR SYSTEMS OF CONSERVATION
LAWS 108 2.3.3 PIECEWISE SMOOTH SOLUTIONS 108 2.3.4 ENTROPY CONDITION
110 2.3.5 PHYSICAL ENTROPY 112 2.3.6 GENERAL PARABOLIC APPROXIMATION AND
THE ENTROPY CONDITION 113 2.3.7 ENTROPY FOR A GENERAL SCALAR
CONSERVATION LAW 115 XIV CONTENTS 2.3.8 ENTROPY FOR A 2 X 2 SYSTEM OF
CONSERVATION LAWS IN ID 117 2.3.9 ENTROPY FUNCTION FOR A P-SYSTEM 118
2.3.10 RIEMANN PROBLEM 118 2.3.11 RIEMANN PROBLEM FOR 2 X 2 ISENTROPIC
GAS DYNAMICS EQUATIONS 120 2.3.12 EXISTENCE AND UNIQUENESS OF ADMISSIBLE
WEAK SOLUTION FOR A SCALAR CONSERVATION LAW 125 2.3.13 PLANE WAVES
ADMITTING DISCONTINUITIES 125 2.3.14 EXISTENCE OF SOLUTIONS TO THE 2X2
EULER SYSTEM FOR AN ISENTROPIC GAS 125 2.3.15 LAX-FRIEDRICHS DIFFERENCE
APPROXIMATIONS 128 2.3.16 EXISTENCE OF APPROXIMATIONS 129 2.3.17
INVARIANT REGIONS FOR RIEMANN INVARIANTS 129 2.3.18 COMPACTNESS ARGUMENT
130 2.3.19 CHARACTERIZATION OF THE WEAK LIMIT BY YOUNG MEASURE 132
2.3.20 DIV-CURL LEMMA AND TARTAR S COMMUTATION RELATION 134 2.3.21
EXISTENCE OF WEAK ENTROPY-ENTROPY FLUX PAIRS 135 2.3.22 LOCALIZATION OF
SUPP V 138 2.3.23 APPROXIMATIVE LIMIT IS AN ADMISSIBLE SOLUTION 144
2.3.24 GLOBAL EXISTENCE FOR GENERAL SYSTEMS IN ONE DIMENSION 145 2.4
FINAL COMMENTS 146 2.4.1 LOCAL EXISTENCE RESULTS 146 2.4.2 GLOBAL SMOOTH
SOLUTIONS 147 2.4.3 BLOW UP AND THE LIFESPAN OF SMOOTH SOLUTION 148
2.4.4 GLOBAL WEAK SOLUTIONS FOR MULTIDIMENSIONAL EULER EQUATIONS 150
2.4.5 RIEMANN PROBLEM 151 2.4.6 EULER EQUATIONS WITH SOURCE TERMS 152
2.4.7 COMMENTS ON THE 2X2 EULER SYSTEM FOR AN ISENTROPIC FLUID 152 2.4.8
EULER EQUATIONS FOR A NONISENTROPIC FLUID 154 3 SOME MATHEMATICAL TOOLS
FOR COMPRESSIBLE FLOWS 155 3.1 RENORMALIZED SOLUTIONS OF THE STEADY
CONTINUITY EQUATION 155 3.1.1 FRIEDRICHS LEMMA ABOUT COMMUTATORS 155
3.1.2 CONTINUITY EQUATION AND ITS PROLONGATION 158 3.1.3 RENORMALIZED
SOLUTIONS OF THE CONTINUITY EQUATION 159 3.2 VECTOR FIELDS WITH SUMMABLE
DIVERGENCE 163 CONTENTS XV 3.3 THE EQUATION DIVV = / 165 3.3.1 BOUNDED
DOMAINS 166 3.3.2 EXTERIOR DOMAINS 176 3.3.3 DOMAINS WITH NONCOMPACT
BOUNDARIES 178 3.4 SOME RESULTS FOR MONOTONE AND CONVEX OPERATORS 183
3.4.1 SOME RESULTS FROM CONVEX ANALYSIS 183 3.4.2 SOME RESULTS FROM
MONOTONE OPERATORS 186 WEAK SOLUTIONS FOR STEADY NAVIER*STOKES EQUATIONS
OF COMPRESSIBLE BAROTROPIC FLOW 189 4.1 FORMULATION OF PROBLEMS IN
BOUNDED AND EXTERIOR DOMAINS AND MAIN RESULTS 189 4.1.1 DEFINITION OF
WEAK SOLUTIONS 190 4.1.2 EXISTENCE OF WEAK SOLUTIONS 192 4.1.3 EXTERIOR
DOMAINS 193 4.2 HEURISTIC APPROACH 194 4.2.1 ESTIMATES DUE TO THE ENERGY
INEQUALITY AND IMPROVED ESTIMATES OF DENSITY 194 4.2.2 LIMIT PASSAGE 195
4.2.3 EFFECTIVE VISCOUS FLUX 196 4.2.4 STRONG CONVERGENCE OF DENSITY -
LIONS APPROACH 197 4.2.5 STRONG CONVERGENCE OF DENSITY - FEIREISL S
APPROACH 198 4.2.6 REMARKS TO APPROXIMATIONS 199 4.3 APPROXIMATIONS IN
BOUNDED DOMAINS 200 4.3.1 FIRST LEVEL APPROXIMATION - ARTIFICIAL
PRESSURE 200 4.3.2 SECOND LEVEL APPROXIMATION - RELAXATION IN THE
CONTINUITY EQUATION 202 4.3.3 THIRD LEVEL APPROXIMATION - RELAXED
CONTINUITY EQUATION WITH DISSIPATION 203 4.4 EFFECTIVE VISCOUS FLUX 204
4.4.1 RIESZ OPERATORS 205 4.4.2 DIV-CURL LEMMA 206 4.4.3 COMMUTATOR
LEMMA 207 4.4.4 EFFECTIVE VISCOUS FLUX 208 4.5 NEUMANN PROBLEM FOR THE
LAPLACIAN 211 4.5.1 EXISTENCE, UNIQUENESS AND REGULARITY 211 4.5.2
EIGENVALUE PROBLEM 212 4.6 RELAXED CONTINUITY EQUATION WITH DISSIPATION
212 4.6.1 STATEMENT OF THE PROBLEM AND RESULTS 212 4.6.2 ESTIMATES FOR
THE LERAY-SCHAUDER FIXED POINTS 213 4.6.3 HOMOTOPY OF COMPACT
TRANSFORMATIONS 215 4.6.4 NONNEGATIVITY OF THE DENSITY 216 4.7 THE LAME
SVSTEM 216 CONTENTS 4.7.1 EXISTENCE, UNIQUENESS AND REGULARITY 217 4.7.2
EIGENVALUE PROBLEM 217 4.8 COMPLETE SYSTEM WITH DISSIPATION IN THE
RELAXED CONTINUITY EQUATION AND WITH ARTIFICIAL PRESSURE 218 4.8.1
EXISTENCE OF SOLUTIONS 218 4.8.2 ESTIMATES INDEPENDENT OF DISSIPATION
222 4.9 COMPLETE SYSTEM WITH RELAXED CONTINUITY EQUATION AND WITH
ARTIFICIAL PRESSURE 223 4.9.1 VANISHING DISSIPATION LIMIT 224 4.9.2
EFFECTIVE VISCOUS FLUX 225 4.9.3 RENORMALIZED CONTINUITY EQUATION WITH
POWERS 226 4.9.4 STRONG CONVERGENCE OF THE DENSITY 230 4.9.5 EQUATION OF
MOMENTUM, ENERGY INEQUALITY AND ESTIMATES INDEPENDENT OF THE RELAXATION
PARAMETER 231 4.10 COMPLETE SYSTEM WITH ARTIFICIAL PRESSURE 231 4.10.1
VANISHING RELAXATION LIMIT 232 4.10.2 EFFECTIVE VISCOUS FLUX 233 4.10.3
RENORMALIZED CONTINUITY EQUATION WITH POWERS 234 4.10.4 STRONG
CONVERGENCE OF THE DENSITY 235 4.10.5 MOMENTUM EQUATION 236 4.10.6
ENERGY INEQUALITY AND ESTIMATES INDEPENDENT OF ARTIFICIAL PRESSURE 236
4.11 COMPLETE SYSTEM OF A VISCOUS BAROTROPIC GAS 239 4.11.1 VANISHING
ARTIFICIAL PRESSURE LIMIT 239 4.11.2 EFFECTIVE VISCOUS FLUX 241 4.11.3
BOUNDEDNESS OF OSCILLATIONS OF DENSITY SEQUENCE 241 4.11.4 RENORMALIZED
CONTINUITY EQUATION 243 4.11.5 STRONG CONVERGENCE OF THE DENSITY 244
4.12 APPROXIMATIONS IN AN EXTERIOR DOMAIN 245 4.12.1 RELAXATION ON
INVADING DOMAINS 245 4.13 COMPLETE SYSTEM WITH RELAXED CONTINUITY
EQUATION ON AN EXTERIOR DOMAIN 247 4.13.1 SOME EQUIVALENCE INEQUALITIES
247 4.13.2 BOUNDS DUE TO THE ENERGY INEQUALITY 247 4.13.3 ESTIMATES
INDEPENDENT OF INVADING DOMAINS AND RELAXATION 248 4.14 EXISTENCE OF
WEAK SOLUTIONS IN EXTERIOR DOMAINS 254 4.14.1 VANISHING RELAXATION LIMIT
254 4.14.2 EFFECTIVE VISCOUS FLUX AND RENORMALIZED CONTINUITY EQUATION
255 4.15 EXISTENCE OF WEAK SOLUTIONS IN BOUNDED AND IN EXTERIOR
LIPSCHITZ DOMAINS 259 CONTENTS XVII 4.16 EXISTENCE OF WEAK SOLUTIONS IN
DOMAINS WITH NONCOMPACT BOUNDARIES 261 4.16.1 FORMULATION OF THE
PROBLEM, FLUXES 262 4.16.2 MAIN RESULTS 264 4.16.3 DOMAINS WITH CONICAL
OR SUPERCONICAL EXITS 265 4.16.4 DOMAINS WITH CYLINDRICAL OR SUBCONICAL
EXITS 268 4.17 FURTHER RESULTS, COMMENTS AND BIBLIOGRAPHIC REMARKS 268
4.17.1 WEAK COMPACTNESS 268 4.17.2 BOUNDED DOMAINS 269 4.17.3 EXTERIOR
DOMAINS 274 4.17.4 DOMAINS WITH NONCOMPACT BOUNDARIES 275 4.17.5 FLOW OF
MIXTURES 278 STRONG SOLUTIONS FOR STEADY NAVIER*STOKES EQUATIONS OF
COMPRESSIBLE BAROTROPIC FLOW AND SMALL DATA 279 5.1 NOTATION AND MAIN
RESULTS 279 5.1.1 FORMULATION OF THE PROBLEM 279 5.1.2 EXISTENCE THEOREM
IN A BOUNDED DOMAIN 280 5.1.3 FUNCTIONAL SPACES FOR EXTERIOR DOMAINS 280
5.1.4 EXISTENCE THEOREMS IN EXTERIOR DOMAINS 281 5.2 HEURISTIC APPROACH
282 5.2.1 PERTURBATIONS AND LINEARIZATION OF THE PROBLEM 282 5.2.2
HELMHOLTZ DECOMPOSITION AND EFFECTIVE VISCOUS FLUX 283 5.2.3 EXISTENCE
THEOREM FOR THE LINEARIZED SYSTEM 285 5.3 AUXILIARY LINEAR PROBLEMS 285
5.3.1 NEUMANN PROBLEM FOR THE LAPLACIAN 286 5.3.2 HELMHOLTZ
DECOMPOSITION 286 5.3.3 DIRICHLET PROBLEM FOR THE LAPLACIAN 287 5.3.4
STOKES AND OSEEN PROBLEMS 287 5.3.5 STEADY TRANSPORT EQUATION 289 5.4
THE LINEARIZED SYSTEM 290 5.5 THE FULLY NONLINEAR SYSTEM 292 5.5.1 THE
CASE OF ZERO VELOCITY AT INFINITY 292 5.5.2 THE CASE OF NONZERO VELOCITY
AT INFINITY 295 5.6 BIBLIOGRAPHIC REMARKS 296 5.6.1 BOUNDED DOMAINS 296
5.6.2 EXTERIOR DOMAINS 297 SOME MATHEMATICAL TOOLS FOR NONSTEADY
EQUATIONS 300 6.1 SOME AUXILIARY RESULTS FROM FUNCTIONAL ANALYSIS 300
6.1.1 CONTINUOUS FUNCTIONS WITH VALUES IN ^ EAK 300 6.1.2 THE TIME AND
SPACE MOLLIFIERS 303 6.1.3 LOCAL WEAK COMPACTNESS IN UNBOUNDED DOMAINS
304 6.2 RENORMALIZED SOLUTIONS OF THE CONTINUITY EQUATION 304 XVIII
CONTENTS 6.2.1 FRIEDRICHS LEMMA ABOUT COMMUTATORS 304 6.2.2 CONTINUITY
EQUATION AND ITS PROLONGATION 306 6.2.3 RENORMALIZED CONTINUITY EQUATION
307 6.2.4 STRONG CONTINUITY OF THE DENSITY 310 7 WEAK SOLUTIONS FOR
NONSTEADY NAVIER-STOKES EQUATIONS OF COMPRESSIBLE BAROTROPIC FLOW 312
7.1 FORMULATION OF PROBLEMS AND MAIN RESULTS 312 7.1.1 DEFINITION OF
WEAK SOLUTIONS 313 7.1.2 EXISTENCE IN BOUNDED DOMAINS 318 7.1.3
EXISTENCE IN EXTERIOR DOMAINS 320 7.2 LINEAR MOMENTUM AND TOTAL ENERGY
321 7.2.1 LINEAR MOMENTUM 321 7.2.2 TOTAL ENERGY 322 7.3 HEURISTIC
APPROACH 324 7.3.1 COMPACTNESS OF WEAK SOLUTIONS 324 7.3.2 ESTIMATES DUE
TO THE ENERGY INEQUALITY 325 7.3.3 IMPROVED ESTIMATE OF THE DENSITY 325
7.3.4 LIMIT PASSAGE 326 7.3.5 EFFECTIVE VISCOUS FLUX 326 7.3.6 STRONG
CONVERGENCE OF DENSITY - LIONS APPROACH 327 7.3.7 STRONG CONVERGENCE OF
DENSITY - FEIREISL S APPROACH 328 7.3.8 REMARKS ON APPROXIMATIONS 329
7.4 APPROXIMATIONS IN BOUNDED DOMAINS 330 7.4.1 FIRST LEVEL
APPROXIMATIONS - ARTIFICIAL PRESSURE 330 7.4.2 SECOND LEVEL
APPROXIMATION - CONTINUITY EQUATION WITH DISSIPATION 333 7.4.3 THIRD
LEVEL APPROXIMATION - GALERKIN METHOD 335 7.5 EFFECTIVE VISCOUS FLUX 338
7.6 CONTINUITY EQUATION WITH DISSIPATION 343 7.6.1 REGULARITY FOR THE
PARABOLIC NEUMANN PROBLEM 343 7.6.2 CONTINUITY EQUATION WITH DISSIPATION
345 7.6.3 CONSTRUCTION OF A SOLUTION - GALERKIN METHOD 346 7.6.4
REGULARITY OF SOLUTIONS 348 7.6.5 BOUNDEDNESS FROM BELOW AND FROM ABOVE
348 7.6.6 L 2 -ESTIMATES 349 7.6.7 L 2 -ESTIMATE OF DIFFERENCES 350
7.6.8 A RENORMALIZED INEQUALITY WITH DISSIPATION 351 7.7 GALERKIN
APPROXIMATION OF THE SYSTEM WITH DISSIPATION IN THE CONTINUITY EQUATION
AND WITH ARTIFICIAL PRESSURE 352 7.7.1 PREPARATORY CALCULATIONS 352
7.7.2 GALERKIN APPROXIMATION 353 CONTENTS XIX 7.7.3 LOCAL EXISTENCE OF
SOLUTIONS 354 7.7.4 EXISTENCE OF MAXIMAL SOLUTIONS 357 7.7.5 ENERGY
INEQUALITIES AND ESTIMATES 360 7.8 COMPLETE SYSTEM WITH DISSIPATION IN
THE CONTINUITY EQUATION AND WITH ARTIFICIAL PRESSURE 361 7.8.1 LIMIT IN
THE MODIFIED CONTINUITY EQUATION 362 7.8.2 LIMIT IN THE MOMENTUM
EQUATION 363 7.8.3 LIMIT IN THE ENERGY INEQUALITY AND ESTIMATES
INDEPENDENT OF VANISHING DISSIPATION 365 7.8.4 IMPROVED ESTIMATE OF
DENSITY 366 7.9 COMPLETE SYSTEM WITH ARTIFICIAL PRESSURE 368 7.9.1 WEAK
LIMITS AS DISSIPATION TENDS TO ZERO 369 7.9.2 EFFECTIVE VISCOUS FLUX 372
7.9.3 RENORMALIZED EQUATION OF CONTINUITY AND STRONG CONVERGENCE OF
DENSITY 374 7.9.4 ENERGY INEQUALITY AND ESTIMATES INDEPENDENT OF
ARTIFICIAL PRESSURE 376 7.9.5 IMPROVED ESTIMATE OF DENSITY 376 7.10
COMPLETE SYSTEM OF ISENTROPIC NAVIER-STOKES EQUATIONS 381 7.10.1 WEAK
LIMITS AT VANISHING ARTIFICIAL PRESSURE 382 7.10.2 EFFECTIVE VISCOUS
FLUX 386 7.10.3 AMPLITUDE OF OSCILLATIONS 386 7.10.4 RENORMALIZED
CONTINUITY EQUATION 388 7.10.5 STRONG CONVERGENCE OF THE DENSITY 390
7.10.6 ENERGY INEQUALITIES 392 7.10.7 GENERAL INITIAL CONDITIONS 392
7.11 EXISTENCE OF SOLUTIONS IN EXTERIOR DOMAINS 393 7.11.1 SOLUTIONS ON
INVADING DOMAINS 393 7.11.2 ORLICZ SPACES LJ(FI) 395 7.11.3 ESTIMATES
INDEPENDENT OF INVADING DOMAINS 396 7.11.4 IMPROVED ESTIMATES OF DENSITY
397 7.11.5 WEAK LIMITS AT GROWING INVADING DOMAINS 398 7.11.6 EFFECTIVE
VISCOUS FLUX AND RENORMALIZED CONTINUITY EQUATION 400 7.11.7 STRONG
CONVERGENCE OF THE DENSITY 401 7.11.8 ENERGY INEQUALITY 404 7.12 OTHER
PROBLEMS AND BIBLIOGRAPHIC REMARKS 404 7.12.1 BIBLIOGRAPHIC REMARKS ON
BASIC THEOREMS 404 7.12.2 SLIP BOUNDARY CONDITIONS 408 7.12.3
NONMONOTONE PRESSURE 409 7.12.4 DOMAIN DEPENDENCE 410 7.12.5
NONHOMOGENEOUS BOUNDARY CONDITIONS 412 7.12.6 UNBOUNDED DOMAINS AND
NON-ZERO VELOCITY AT INFINITY 424 XX CONTENTS 7.12.7 DOMAINS WITH
NONSMOOTH BOUNDARIES 429 8 GLOBAL BEHAVIOR OF WEAK SOLUTIONS 431 8.1
FORMULATION OF THE PROBLEM 431 8.2 BASIC ASSUMPTIONS 432 8.3 SEQUENTIAL
STABILIZATION OF THE WEAK SOLUTION 432 8.4 AUXILIARY FUNCTIONS 433 8.5
EXISTENCE AND ESTIMATES OF AUXILIARY FUNCTIONS 435 8.6 COMPARISON
DENSITY AND A TEST FUNCTION 437 8.7 PASSING TO THE LIMIT WITH THE
REGULARIZATION PARAMETER 437 8.8 COMPARISON DENSITY IS CLOSE TO THE
DENSITY AS T * * OO. 438 8.9 CONVERGENCE OF THE DENSITY 446 8.10
UNIQUENESS OF EQUILIBRIUM 452 8.11 GLOBAL BEHAVIOR OF WEAK SOLUTIONS IN
TIME IN BOUNDED DOMAINS - ARBITRARY FORCES 456 8.12 BOUNDED ABSORBING
SETS 457 8.13 ASYMPTOTICALLY CLOSED TRAJECTORIES 458 8.14 GLOBAL
ATTRACTOR OF SHORT TRAJECTORIES 459 8.15 RAPIDLY OSCILLATING EXTERNAL
FORCES 460 8.16 ATTRACTORS 460 8.17 TIME-PERIODIC SOLUTIONS 461 8.18
UNIQUENESS OF EQUILIBRIUM REVISITED 462 9 STRONG SOLUTIONS OF NONSTEADY
COMPRESSIBLE NAVIER*STOKES EQUATIONS 464 9.1 PROBLEM FORMULATION 464 9.2
SIMILARITY TRANSFORMATION 465 9.3 MAXIMAL PARABOLIC REGULARITY 466 9.4
RESOLUTION OF THE CONTINUITY EQUATION WITH A GIVEN VELOCITY 467 9.5
FURTHER TRANSCRIPTION OF THE PROBLEM 469 9.6 FIXED POINT ARGUMENT AND
THE EXISTENCE OF A LOCAL SOLUTION 470 9.7 UNIQUENESS 473 9.8 GLOBAL A
PRIORI ESTIMATE 474 9.9 GLOBAL EXISTENCE 479 9.10 BIBLIOGRAPHICAL
REMARKS 480 REFERENCES 485 INDEX 499
|
| any_adam_object | 1 |
| author | Novotný, Antonín Straškraba, Ivan |
| author_facet | Novotný, Antonín Straškraba, Ivan |
| author_role | aut aut |
| author_sort | Novotný, Antonín |
| author_variant | a n an i s is |
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| bvnumber | BV019310399 |
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| callnumber-raw | QA911 |
| callnumber-search | QA911 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 |
| classification_tum | MTA 309f PHY 227f |
| ctrlnum | (OCoLC)55970071 (DE-599)BVBBV019310399 |
| dewey-full | 620.1/064/015118 532.51 |
| dewey-hundreds | 600 - Technology (Applied sciences) 500 - Natural sciences and mathematics |
| dewey-ones | 620 - Engineering and allied operations 532 - Fluid mechanics |
| dewey-raw | 620.1/064/015118 532.51 |
| dewey-search | 620.1/064/015118 532.51 |
| dewey-sort | 3620.1 264 515118 |
| dewey-tens | 620 - Engineering and allied operations 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV019310399 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:57:21Z |
| institution | BVB |
| isbn | 0198530846 9780198530848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012778218 |
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| physical | XX, 506 S. |
| publishDate | 2004 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Novotný, Antonín Verfasser aut Introduction to the mathematical theory of compressible flow A. Novotný ; I. Straškraba 1. publ. Oxford [u.a.] Oxford Univ. Press 2004 XX, 506 S. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 27 Mathematisches Modell Compressibility Fluid dynamics Mathematical models Kompressible Strömung (DE-588)4032018-2 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Kompressible Strömung (DE-588)4032018-2 s Mathematische Methode (DE-588)4155620-3 s DE-604 Straškraba, Ivan Verfasser aut Oxford lecture series in mathematics and its applications 27 (DE-604)BV009910017 27 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012778218&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Novotný, Antonín Straškraba, Ivan Introduction to the mathematical theory of compressible flow Oxford lecture series in mathematics and its applications Mathematisches Modell Compressibility Fluid dynamics Mathematical models Kompressible Strömung (DE-588)4032018-2 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4032018-2 (DE-588)4155620-3 |
| 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. Straškraba |
| title_fullStr | Introduction to the mathematical theory of compressible flow A. Novotný ; I. Straškraba |
| title_full_unstemmed | Introduction to the mathematical theory of compressible flow A. Novotný ; I. Straškraba |
| title_short | Introduction to the mathematical theory of compressible flow |
| title_sort | introduction to the mathematical theory of compressible flow |
| topic | Mathematisches Modell Compressibility Fluid dynamics Mathematical models Kompressible Strömung (DE-588)4032018-2 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Mathematisches Modell Compressibility Fluid dynamics Mathematical models Kompressible Strömung Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012778218&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009910017 |
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