The first monograph on the mathematical theory of shape optimization for compressible Navier-Stokes equations, this publication offers clear explanations of cutting-edge developments in a mathematical language that will foster research in this important field.
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.
Inhaltsverzeichnis
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.
