Singular Limits in Thermodynamics of Viscous Fluids (eBook)

Eduard Feireisl, Antonín Novotný (Autoren)

eBook Download: PDF

2017 | 2nd ed. 2017
XLII, 524 Seiten
Springer International Publishing (Verlag)
978-3-319-63781-5 (ISBN)

Infos

This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids.

'The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits.'
Milan Pokorný (zbMATH)

'This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament

al importance. It is self-contained, thanks to Chapter 3 (existence theory) and to the appendices. It is extremely well organized, and very well written. It is a landmark for researchers in mathematical fluid dynamics, especially those interested in the physical meaning of the equations and statements.'
Denis Serre (MathSciNet)

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 24.11.2017
• Reihe/Serie: Advances in Mathematical Fluid Mechanics
• Reihe/Serie: Advances in Mathematical Fluid Mechanics
• Zusatzinfo: XLII, 524 p.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Dissipation • Fluid Dynamics • fluid mechanics • Magnetohydrodynamics • Navier-Stokes-Fourier • Nonlinear Systems • partial differential equation • Partial differential equations • Rhe • Single Limits • thermodynamics • viscous fluids
• ISBN-10: 3-319-63781-9 / 3319637819
• ISBN-13: 978-3-319-63781-5 / 9783319637815