Navier--Stokes--Fourier system with Dirichlet boundary conditions for temperature

Abstract: In this talk, we consider the Navier--Stokes--Fourier system, describing the motion of a compressible, viscous, and heat conducting fluid in a bounded domain $\Omega \subset R^d$, $d =2,3$, with general non-homogeneous Dirichlet boundary conditions for the absolute temperature. We introduce a new concept of weak solution based on the satisfaction of the entropy inequality together with a balance law for the ballistic energy. We show the existence of global-in-time weak solutions, as well as the weak--strong uniqueness principle.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).