Compressible Navier Stokes Equations : Theory and Shape Optimization 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. 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.