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.