Feireisl / Novotný Singular Limits in Thermodynamics of Viscous Fluids

1. Auflage 2009
ISBN: 978-3-7643-8843-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 382 Seiten, eBook

Reihe: Advances in Mathematical Fluid Mechanics

Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux.As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.

Zielgruppe

Research

Autoren/Hrsg.

Feireisl, Eduard

Novotný, Antonín

Inhaltsverzeichnis

Fluid Flow Modeling.- Weak Solutions, A Priori Estimates.- Existence Theory.- Asymptotic Analysis — An Introduction.- Singular Limits — Low Stratification.- Stratified Fluids.- Interaction of Acoustic Waves with Boundary.- Problems on Large Domains.- Acoustic Analogies.- Bibliographical Remarks.