Produktbild: Singular Limits in Thermodynamics of Viscous Fluids

Singular Limits in Thermodynamics of Viscous Fluids

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

31.08.2018

Verlag

Springer

Seitenzahl

524

Maße (L/B/H)

23.5/15.5/3.1 cm

Gewicht

860 g

Auflage

Softcover reprint of the original 2nd edition 2017

Sprache

Englisch

ISBN

978-3-319-87633-7

Beschreibung

Rezension

“This second edition is still intended … to researchers and doctoral students that are interested in the mathematical theory of asymptotic analysis of heat conducting compressible viscous fluids.” (Luisa Consiglieri, zbMATH 1432.76002, 2020)

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

31.08.2018

Verlag

Springer

Seitenzahl

524

Maße (L/B/H)

23.5/15.5/3.1 cm

Gewicht

860 g

Auflage

Softcover reprint of the original 2nd edition 2017

Sprache

Englisch

ISBN

978-3-319-87633-7

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Singular Limits in Thermodynamics of Viscous Fluids
  • Preface.- 1 Fluid flow modeling.- 1.1 Field equations of continuum fluid mechanics.- 1.2 Constitutive relations.- 2 Mathematical theory of weak solutions.- 2.1 Variational formulation.- 2.2 A priori estimates.- 3 Existence theory.- 3.1 Hypotheses.- 3.2 Structural properties of constitutive functions.- 3.3 Main existence result.- 3.4 Solvability of the approximate system.- 3.5 Limit in the Faedo-Galerkin approximation scheme.- 3.6 Artificial diffusion limit.- 3.7 Vanishing artificial pressure.- 3.8 Regularity properties of weak solutions.- 4 Asymptotic analysis - an introduction.- 4.1 Scaling and scaled equations.- 4.2 Low Mach number limit.- 4.3 Strongly satisfied flows.- 4.4 Acoustic waves.- 5 Singular limits - low stratification.- 5.1 Hypotheses and global existence for the primitive system.- 5.2 Dissipation equation, uniform solutions.- 5.3 Convergence.- 5.4 Acoustiv waves.- 5.5 Conclusion - main result.- 6 Stratified fluids.- 6.1 Motivation.- 6.2 Primitive system.- 6.3 Asymptotic limit.- 6.4 Uniform estimates.- 6.5 Convergence towards the target system.- 6.6 Analysis of the acoustic waves.- 6.7 Asymptotic limit in the entropy balance.- 7 Refined analysis of the acoustic waves.- 7.1 Problem formulation.- 7.2 Main result.- 7.3 Uniform estimates.- 7.4 Analysis of the acoustic waves.- 7.5 Strong convergence of the velocity field.- 8 Appendix.- 8.1 Quasilinear parabolic equations.- 8.2 Mollifiers.- 8.3 The normal traces.- 8.4 The Bogovskii Operator.- 8.5 Maximal regularity to parabolic equations.- 8.6 Korn and Poincaré type inequalities.- 8.7 Radon measures.- 8.8 Weak convergence, monotone and convex functions.- 8.9 Fourier and the Riesz transforms.- 8.10 Div-Curl lemma and commutators involving the Riesz operators.- 8.11 Renormalized solutions to the continuity equation.- 9 Bibliographic remarks 9.1 Fluid flow modeling.- 9.2 Mathematical theory of the weak solutions.- 9.3 Singular limits.