Mathematical Topics in Fluid Mechanics: Compressible Models, Vol. 2
This volume and its companion, both written by a winner of the 1994 Fields Medal, provide a unique and rigorous treatise on mathematical aspects of fluid mechanics models. These 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. This second volume focuses on compressible Navier-Stokes equations. It is probably the first reference covering the issue...
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This volume and its companion, both written by a winner of the 1994 Fields Medal, provide a unique and rigorous treatise on mathematical aspects of fluid mechanics models. These 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. This second volume focuses on compressible Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes entirely new 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 one of the most important branches of science, the rigorous mathematical modeling of physical phenomena.
Part II: Compressible models 5. Compactness results for compressible isentropic Navier-Stokes equations6. Stationary problems7. Existence results for Cauchy problems8. 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 2Erratum (Volume 1)Index
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