Compressible Navier-Stokes Equations: Theory and Shape Optimization

The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include:

modeling of compressible viscous flows;

modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations;

applications to optimal shape design in aerodynamics;

kinetic theory for equations with oscillating data;

new approach to the boundary value problems for transport equations.

The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.