Navier-Stokes-Fourier system with Dirichlet boundary conditions

0560286 - MÚ 2023 RIV GB eng J - Journal Article
Chaudhuri, N. - Feireisl, Eduard
Navier-Stokes-Fourier system with Dirichlet boundary conditions.
Applicable Analysis. Roč. 101, č. 12 (2022), s. 4076-4094. ISSN 0003-6811. E-ISSN 1563-504X
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : Dirichlet boundary conditions * Navier-Stokes-Fourier system * weak solution * weak-strong uniqueness
OECD category: Pure mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1080/00036811.2021.1992396

We consider the Navier–Stokes–Fourier system describing the motion of a compressible, viscous, and heat-conducting fluid in a bounded domain (Formula presented.), d = 2, 3, 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 a 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.
Permanent Link: https://hdl.handle.net/11104/0333272