Format:
Online-Ressource (XVI, 457 p. 1 illus. in color, digital)
ISBN:
9783034803670
,
1283624958
,
9781283624954
Series Statement:
Monografie Matematyczne 73
Content:
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.
Content:
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.
Note:
Description based upon print version of record
,
Compressible Navier-Stokes Equations; Theory and Shape Optimization; Contents; Preface; Introduction; Chapter 1 Preliminaries; 1.1 Functional analysis; 1.1.1 Banach spaces; 1.1.2 Interpolation of Banach spaces; 1.1.3 Invertibility of linear operators; 1.1.4 Fixed point theorems; 1.2 Function spaces; 1.2.1 Hölder spaces; Hölder spaces of Banach space valued functions; Arzelà-Ascoli theorem; 1.2.2 Measure and integral; 1.2.3 Lebesgue measure in Rd. Lebesgue spaces; 1.3 Compact sets in Lp spaces; 1.3.1 Functions of bounded variation; 1.3.2 Lp spaces of Banach space valued functions
,
1.4 Young measures1.5 Sobolev spaces; 1.6 Mollifiers and DiPerna & Lions lemma; 1.7 Partial differential equations-selected facts; 1.7.1 Elliptic equations; 1.7.2 Stokes problem; 1.7.3 Parabolic equations; Chapter 2 Physical background; 2.1 Governing equations; 2.1.1 Isentropic flows. Compressible Navier-Stokes equations; 2.2 Boundary and initial conditions; 2.3 Power and work of hydrodynamic forces; 2.4 Navier-Stokes equations in a moving frame; 2.5 Flow around a moving body; Chapter 3 Problem formulation; 3.1 Weak solutions; 3.2 Renormalized solutions
,
3.3 Work functional. Optimization problemChapter 4 Basic statements; 4.1 Introduction; 4.2 Bounded energy functions; 4.3 Functions of bounded mass dissipation rate; 4.4 Compactness properties; 4.4.1 Two lemmas on compensated compactness; 4.4.2 Proof of Theorem 4.4.2; 4.5 Basic integral identity; 4.6 Proof of continuity of viscous flux for general stress tensors; 4.7 Viscous flux. Localization; Chapter 5 Nonstationary case. Existence theory; 5.1 Problem formulation. Results; 5.2 Regularized equations; 5.3 Passage to the limit. The first level; 5.3.1 Step 1. Convergence of densities and momenta
,
5.3.2 Step 2. Weak convergence of the kinetic energy tensor5.3.3 Step 3. Weak limits of ε∇ ϱn ö un; 5.3.4 Step 4. Proof of estimates (5.3.8-5.3.9); 5.3.5 Step 5. Proof of Theorem 5.3.1; 5.3.6 Proof of Theorem 5.3.2; 5.3.7 Local pressure estimate; 5.3.8 Normal derivative of the density; 5.4 Passage to the limit. The second level; 5.5 Passage to the limit. The third level; Chapter 6 Pressure estimate; Chapter 7 Kinetic theory. Fast density oscillations; 7.1 Problem formulation. Main results; 7.2 Proof of Theorem 7.1.9; 7.3 Proof of Theorem 7.1.12
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7.4 Compactness and existence of solutions for adiabatic exponent γ 〉 3/2Chapter 8 Domain convergence; 8.1 Hausdorff and Kuratowski-Mosco convergences; 8.2 Capacity, quasicontinuity and fine topology; 8.3 Applications to flow around an obstacle; 8.4 S-compact classes of admissible obstacles; Chapter 9 Flow around an obstacle. Domain dependence; 9.1 Preliminaries; 9.2 Existence theory; 9.3 Main stability theorem; Chapter 10 Existence theory in nonsmooth domains. Shape optimization, continuity of the work functional; 10.1 Existence theory in nonsmooth domains
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10.2 Continuity of the work functional
Additional Edition:
ISBN 9783034803663
Additional Edition:
Buchausg. u.d.T. Plotnikov, Pavel I. Compressible Navier-Stokes equations Basel : Birkhäuser, 2012 ISBN 3034803664
Additional Edition:
ISBN 9783034803663
Language:
English
Subjects:
Mathematics
Keywords:
Navier-Stokes-Gleichung
;
Kompressible Strömung
;
Navier-Stokes-Gleichung
;
Kompressible Strömung
DOI:
10.1007/978-3-0348-0367-0
URL:
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