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arXiv · 2106.05315

Navier-Stokes-Fourier system with Dirichlet boundary conditions

Nilasis Chaudhuri·Eduard Feireisl
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Abstract

We consider the Navier--Stokes--Fourier system describing the motion of a compressible, viscous, and heat conducting fluid in a bounded domain with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute temperature, with the associated boundary conditions for the density on the inflow part. 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 weak-strong uniqueness principle as well as the existence of global-in-time solutions.

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Nilasis Chaudhuri, Eduard Feireisl. 2021-06-09. Navier-Stokes-Fourier system with Dirichlet boundary conditions. https://arxiv.org/abs/2106.05315

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