Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba.

Includes bibliographical references and index.

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This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to.

1 Fundamental concepts and equations -- 1.1 Some mathematical concepts and notation -- 1.1.1 Basic notation -- 1.1.2 Some useful inequalities in IR[sup(N)] -- 1.1.3 Differential operators -- 1.1.4 Gronwall's lemma -- 1.1.5 Implicit functions -- 1.1.6 Transformations of Cartesian coordinates -- 1.1.7 Hölder-continuous and Lipschitz functions -- 1.1.8 The symbols "o" and "O" -- 1.1.9 Partitions of unity -- 1.1.10 Measure -- 1.1.11 Description of the boundary -- 1.1.12 Measure on the boundary of a domain -- 1.1.13 Classical Green's theorem -- 1.1.14 Lebesgue spaces.

1.1.15 Lebesgue's points -- 1.1.16 Absolutely continuous functions -- 1.1.17 Absolute continuity of integrals with respect to measurable subsets -- 1.1.18 Some theorems from integration theory -- 1.2 Governing equations and relations of gas dynamics -- 1.2.1 Description of the flow -- 1.2.2 The transport theorem -- 1.2.3 The continuity equation -- 1.2.4 The equations of motion -- 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor -- 1.2.6 Inviscid and viscous fluids -- 1.2.7 The energy equation -- 1.2.8 The second law of thermodynamics and the entropy.

1.2.9 Principle of material frame indifference -- 1.2.10 Newtonian fluids -- 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids -- 1.2.12 Entropy form of the energy equation for Newtonian fluids -- 1.2.13 Some consequences of the Clausius-Duhem inequality -- 1.2.14 Equations of state -- 1.2.15 Adiabatic flow of a perfect inviscid gas -- 1.2.16 Compressible Euler equations -- 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas -- 1.2.18 Barotropic flow of a viscous gas -- 1.2.19 Speed of sound -- 1.2.20 Simplified models.

1.2.21 Initial and boundary conditions -- 1.3 Some advanced mathematical concepts and results -- 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions -- 1.3.2 Young's functions, Jensen's inequality -- 1.3.3 Orlicz spaces -- 1.3.4 Distributions -- 1.3.5 Sobolev spaces -- 1.3.6 Homogeneous Sobolev spaces -- 1.3.7 Tempered distributions -- 1.3.8 Radon measure and representation of C[sub(B)](])* -- 1.3.9 Functions of bounded variation -- 1.3.10 Functions with values in Banach spaces -- 1.3.11 Sobolev imbeddings of abstract spaces -- 1.3.12 Some compactness results.

1.4 Survey of concepts and results from functional analysis -- 1.4.1 Linear vector spaces -- 1.4.2 Topological linear spaces -- 1.4.3 Metric linear space -- 1.4.4 Normed linear space -- 1.4.5 Duals to Banach spaces and weak( -*) topologies -- 1.4.6 Riesz representation theorem -- 1.4.7 Operators -- 1.4.8 Elements of spectral theory -- 1.4.9 Lax-Milgram lemma -- 1.4.10 Imbeddings -- 1.4.11 Solution of nonlinear operator equations -- 2 Theoretical results for the Euler equations -- 2.1 Hyperbolic systems and the Euler equations -- 2.1.1 Zero-viscosity Burgers equation.

English.

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