Stationary solutions in thermodynamics of stochastically forced fluids

Dominic Breit, Eduard Feireisl, Martina Hofmanová

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We study the full Navier–Stokes–Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary conditions for the temperature and hence energetically open. We show that, in contrast with the energetically closed system, there exists a stationary solution. Our approach is based on new global-in-time estimates which rely on the non-homogeneous boundary conditions combined with estimates for the pressure.
Original languageEnglish
Pages (from-to)1127–1155
Number of pages29
JournalMathematische Annalen
Early online date19 Nov 2021
Publication statusPublished - Dec 2022

ASJC Scopus subject areas

  • General Mathematics


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