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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Mathematical Thermodynamics of Viscous Fluids
 Feireisl, Eduard
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.
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On the motion of chemically reacting fluids through porous medium
 Feireisl, Eduard ; Mikyška, J. ; Petzeltová, Hana ; Takáč, P.
We consider a parabolic-hyperbolic system of nonlinear partial differential equations modeling the motion of a chemically reacting mixture through porous medium. The existence of classical as well as weak solutions is established under several physically relevant choices of the constitutive equations and relevant boundary conditions.
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