Original title: Mathematical Thermodynamics of Viscous Fluids
Authors: Feireisl, Eduard
Document type: Papers
Conference/Event: CIME Summer School on Mathematical Thermodynamics of Complex Fluids, Cetraro (IT), 20150629
Year: 2017
Language: eng
Abstract: This course is a short introduction to the mathematical theory of the motion of viscous fluids. We introduce the concept of weak solution to the Navier-Stokes-Fourier system and discuss its basic properties. In particular, we construct the weak solutions as a suitable limit of a mixed numerical scheme based on a combination of the finite volume and finite elements method. The question of stability and robustness of various classes of solutions is addressed with the help of the relative (modulated) energy functional. Related results concerning weak-strong uniqueness and conditional regularity of weak solutions are presented. Finally, we discuss the asymptotic limit when viscosity of the fluid tends to zero. Several examples of ill- posedness for the limit Euler system are given and an admissibility criterion based on the viscous approximation is proposed.
Keywords: Navier-Stokes-Fourier system; thermodynamics of viscous fluid
Project no.: 320078
Host item entry: Mathematical Thermodynamics of Complex Fluids, ISBN 978-3-319-67599-2, ISSN 0075-8434
Note: Související webová stránka: https://link.springer.com/chapter/10.1007%2F978-3-319-67600-5_2

Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0278911

Permalink: http://www.nusl.cz/ntk/nusl-373337


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Research > Institutes ASCR > Institute of Mathematics
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