Ebook: Compressible Navier-Stokes Equations: Theory and Shape Optimization
- Tags: Partial Differential Equations, Mathematical Physics
- Series: Monografie Matematyczne 73
- Year: 2012
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
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
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.
Content:
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
....