Many problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations. This book is an introduction to the problems involving singular limits based on the concept of weak or variational solutions.

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)

This is a second edition with include updated material and developments This book gives an introduction to the problems involving singular limits based on the concept of weak or variational solutions This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids

Autorentext
Eduard Feireisl is a senior research worker at the Institute of Mathematics of the Czech Academy of Sciences and full professor at Charles University in Prague. He authored or coauthored 7 research monographs and over 300 research papers registered by the database MathSciNet. His main research interest is the abstract theory of partial differential equations with application in fluid mechanics, including numerical analysis and the effect of stochastic phenomena. He is one of the leading experts in the field of mathematical fluid mechanics. Mária Luká ová-Medvi ová is professor for Applied Mathematics at the Johannes Gutenberg-University Mainz. She is a vice speaker of the Research Center Multiscale Simulation Methods for Soft Matter Systems and of the Mainz Institute for Multiscale Modeling. Her research interests lay in numerics and analysis of partial differential equations. She made important contributions to the development of structure-preserving schemes for hyperbolic conservation laws and hybrid multiscale methods for complex fluids. She received various awards, such as the Prize of the Czech Learned Society in 2002, Bronze Medal of the University of Koice in 2013, or the Gutenberg Research College Fellowship in 2020. Hana Mizerová is an assistant professor at the Department of Mathematical Analysis and Numerical Mathematics of Comenius University in Bratislava, Slovakia. Her research focuses on numerical analysis of partial differential equations in fluid mechanics. In 2018, she was awarded the Seal of Excellence by the European Commission. Bangwei She is a research worker at the Institute of Mathematics of the Czech Academy of Sciences. His research interests are in numerical analysis and scientific computing, particularly for partial differential equations with a focus on computational fluid dynamics.

Inhalt

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.