Mathematical Thermodynamics of Viscous Fluids

0483709 - MÚ 2018 RIV CH eng C - Conference Paper (international conference)
Feireisl, Eduard
Mathematical Thermodynamics of Viscous Fluids.
Mathematical Thermodynamics of Complex Fluids. Cham: Springer, 2017 - (Feireisl, E.; Rocca, E.), s. 47-100. Lecture Notes in Mathematics, 2200. ISBN 978-3-319-67599-2. ISSN 0075-8434. E-ISSN 1617-9692.
[CIME Summer School on Mathematical Thermodynamics of Complex Fluids. Cetraro (IT), 29.06.2015-03.07.2015]
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : thermodynamics of viscous fluid * Navier-Stokes-Fourier system
OECD category: Pure mathematics
https://link.springer.com/chapter/10.1007%2F978-3-319-67600-5_2

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.
Permanent Link: http://hdl.handle.net/11104/0278911