Compressible Navier-Stokes equations: theory and shape optimization

✍ Scribed by Pavel Plotnikov, Jan Sokołowski (auth.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 470
• Series: Monografie Matematyczne 73
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Preliminaries....Pages 1-44
Physical background....Pages 45-55
Problem formulation....Pages 57-61
Basic statements....Pages 63-97
Nonstationary case. Existence theory....Pages 99-166
Pressure estimate....Pages 167-173
Kinetic theory. Fast density oscillations....Pages 175-224
Domain convergence....Pages 225-248
Flow around an obstacle. Domain dependence....Pages 249-280
Existence theory in nonsmooth domains. Shape optimization, continuity of the work functional....Pages 281-298
Sensitivity analysis. Shape gradient of the drag functional....Pages 299-376
Boundary value problems for transport equations....Pages 377-406
Appendix....Pages 407-440
Back Matter....Pages 441-457

✦ Subjects

Partial Differential Equations; Mathematical Physics