Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

• Part II: Compressible models


• 5: Compactness results for compressible isentropic Navier-Stokes equations


• 6: Stationary problems


• 7: Existence results for Cauchy problems


• 8: Related problems


• Appendix A. A few facts about some function spaces


• Appendix B. On a weakly continuous product


• Appendix C. A remark on the limiting case for Sobolev inequalities


• Appendix D. Continua and limits


• Appendix E. On sums of Lp spaces


• Appendix F. A remark on parabolic equations


• Bibliography of Volumes 1 and 2


• Erratum (Volume 1)


• Index

Professor of Mathematics at University Paris-Dauphine and of Applied Mathematics at Ecole Polytechnique. Address to which correspondence should be sent: CEREMADE - URA CNRS 749, Universite Paris-Dauphine, Place de Lattre de Tassigny, F - 75775 Paris Cedex 16, France