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Compressible Navier-Stokes Equations [electronic resource] : Theory and Shape Optimization / by Pavel Plotnikov, Jan Sokołowski.

By: Plotnikov, Pavel [author.].
Contributor(s): Sokołowski, Jan [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Monografie Matematyczne: 73Publisher: Basel : Springer Basel : Imprint: Birkhäuser, 2012Description: XVI, 457 p. 1 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783034803670.Subject(s): Mathematics | Differential equations, partial | Mathematics | Partial Differential Equations | Mathematical PhysicsDDC classification: 515.353 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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