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Mathematical Topics in Fluid Mechanics : Volume 2 -Compressible Models: Oxford Lecture Series in Mathematics and Its Applications , Vol 2, No 10

Pierre-Louis Lions

A mathematical analysis of compressible models.

Bookcover

Format: Hardcover, English, 348 pages
ISBN: 0198514883
Publisher: Oxford University Press
Pub. Date: 1998

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Table of Contents

5 Compactness results for compressible isentropic Navier-Stokes equations
5.1 Preliminaries
5.2 Compactness results and propagation of oscillations
5.3 Proofs of compactness results in the whole space case
5.4 Proofs of compactness results in the other cases
5.5 General pressure laws
5.6 Other boundary value problems
6 Stationary problems
6.1 Preliminaries
6.2 Existence and regularity results for time-discretized problems
6.3 A priori estimates
6.4 Compactness
6.5 Existence proofs
6.6 The isothermal case in two dimensions
6.7 Stationary problems
6.8 Exterior problems and related questions
6.9 Regularity of solutions
6.10 Related problems
6.11 General compressible models
7 Existence results for Cauchy problems
7.1 A priori bounds
7.2 Existence results
7.3 Existence proofs via regularization
7.4 Existence proofs via time discretization
7.5 General pressure laws
7.6 Other boundary-value problems
8 Related problems
8.1 Pure transport of entropy
8.2 A semi-stationary model
8.3 A Stokes-like model
8.4 On some shallow water models
8.5 Compactness properties for compressible models with temperature
8.6 Global existence results for some compressible models with temperature
8.7 On compressible Euler equations
8.8 On a low Mach number model
Appendix A: A few facts about some function spaces
Appendix B: On a weakly continuous product
Appendix C: A remark on the limiting case of Sobolev inequalities
Appendix D: Continua and limits
Appendix E: On sums of L(p) spaces
Appendix F: A remark on parabolic equations
Bibliography
Errata (Volume 1)
Index

Related Book Categories

Basic Fluid Dynamics, Compressible Flow, Numerical Methods


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