This series of books forms 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 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 the great theoretical problems in science concerning rigorous
mathematical modelling of physical phenomena. Pierre-Louis Lions is
Professor of Mathematics at the University Paris-Dauphine and of
Applied Mathematics at the Ecole Polytechnique.
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