The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on 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.

Contenu

Preface.- Introduction.- 1 Preliminaries.- 2 Physical background.- 3 Problem formulation.- 4 Basic statements.- 5 Nonstationary case. Existence theory.- 6 Pressure estimate.- 7 Kinetic theory. Fast density oscillations.- 8 Domain convergence.- 9 Flow around an obstacle. Domain dependence.- 10 Existence theory in nonsmooth domains.- 11 Sensitivity analysis. Shape gradient of the drag functional.- 12 Transport equations.- 13 Appendix.- Bibliography.- Notation.- Index.