Stochastic Navier-Stokes-Fourier equations

Dominic Breit, Eduard Feireisl

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Abstract

We study the full Navier-Stokes-Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise, (iii) random heat source in the internal energy balance. We establish existence of a weak martingale solution under physically grounded structural assumptions. As a byproduct of our theory we can show that stationary martingale solutions only exist in certain trivial cases.
Original languageEnglish
Pages (from-to)911-975
Number of pages65
JournalIndiana University Mathematics Journal
Volume69
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Compressible fluids
  • Heat-conducting fluid
  • Martingale solution
  • Stochastic Navier-Stokes-Fourier system
  • Weak solution

ASJC Scopus subject areas

  • Mathematics(all)

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