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Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Reprint of the 1998 hardback ed. (English) Zbl 1264.76003
Oxford: Clarendon Press (ISBN 978-0-19-967922-5/pbk). 364 p. (2013).
Publisher’s description: 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, the book 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.
See the review of the hardback edition in [Zbl 0908.76004]. For the first volume see [Zbl 1264.76002].

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics