Lectures on the Analysis of Nonlinear Partial Differential Equations

0369962 - MÚ 2012 RIV CN eng M - Monography Chapter
Feireisl, Eduard
Scale analysis of complete fluid systems.
Lectures on the Analysis of Nonlinear Partial Differential Equations. Vol.2. 1. Beijing: Higher Education Press, 2011 - (Lin, F.; Zhang, P.), s. 47-86. Morningside Lectures in Mathematics. ISBN 978-7-04-031610-0
R&D Projects: GA ČR GA201/08/0315
Institutional research plan: CEZ:AV0Z10190503
Keywords : scale analysis * Navier-Stokes-Fourier system * Oberbeck-Boussinesq system * incompressible limit
Subject RIV: BA - General Mathematics

This is a survey on some recently developed mathematical methods in the scale analysis of the full Navier-Stokes-Fourier system, in particular, the so-called incompressible limits, where the target system is represented by the incompressible Navier-Stokes equations supplemented with an equation describing the transfer of heat. We introduce a general framework based on the concept of weak solutions, discuss the effect of acoustic waves and their dispersion on large physical domains, and illustrate the abstract methods by a rigorous derivation of the Oberbeck-Boussinesq approximation on an exterior domain.
Permanent Link: http://hdl.handle.net/11104/0203898