Contributing to the mathematical theory of the fluids, Feireisl (mathematics, Academy of Sciences, the Czech Republic) describes global existence results for the full system of the Navier-Stokes equations with large data supplemented with a suitable set of constitutive equations, and optimal existence results for the barotropic flows with respect to the available a priori estimates. He also introduces two new tools: an oscillations defect measure to obtain a more precise description of possible oscillations of the density component in a sequence of approximate solutions; and a renormalized limit of a sequence of bounded integrable functions to cope with possible concentrations in the temperature. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
The book develops the most recent ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. Two main goals are pursued: (I) global existence theory within the framework of variational (weak) solutions for the full system of the Navier-Stokes equations supplemented with large data; and (II) optimal existence results for the barotropic flows with respect to the available a priori estimates. The book is intended to be a compact and self-contained presentation of the most recent results of the mathematical theory of viscous compressible fluids. In order to place the text in better perspective, each chapter is concluded with a section devoted to historical notes including references to all-important and new results. The material is by no means intended to be the last word on the subject but rather to include possible directions of future research. It is aimed at research mathematicians, theoretical physicists, engineers and graduate students.
