Compressible Navier-Stokes Equations : Theory and Shape Optimization (Monografie Matematyczne Vol.73) (2012. xvi, 464 S. 1 Farbabb.,. 23,5 cm)

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. Preface.- 1 Preliminaries.- 2 Physical backgrounds.- 3 Problem formulation.- 4 Basic statements.- 5 Non stationary case. Existence theory.- 6 Pressure estimate.- 7 Kinetic theory. Fast density oscillations.-8 Shape sensitivity analysis of non stationary problems.- 9 Shape sensitivity analysis of stationary problems.- 10 Boundary value problems for transport equations.- 11 Appendix.- Bibliography.