Mathematical Topics in Fluid Mechanics Volume 2: Compressible Models

This second volume works with the first to form a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations such as the incompressible and compressible NavierStokes equations. The main emphasis in the first volume is on the mathematical analysis of incompressible models. The second volume is an attempt to achieve a mathematical understanding of compressible Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes unique material on compactness properties of solutions for the Cauchy problem, the existence and regularity of stationary solutions, and the existence of global weak solutions. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena.

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 L^p spaces
Appendix F. A remark on parabolic equations
Bibliography of Volumes 1 and 2
Erratum (Volume 1)
Index