Compressible Navier-Stokes system with transport noise

Dominic Breit, Eduard Feireisl, Martina Hofmanová, Ewelina Zatorska

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We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both a continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the equations are understood as in the sense of the classical weak deterministic theory, (ii) the noise is rough in time and we interpret the equations in the framework of rough paths with unbounded rough drivers, and (iii) we have a Brownian noise of Stratonovich type and study the existence of martingale solutions. The first situation serves as an approximation for (ii) and (iii), while (ii) and (iii) are motivated by recent results on the incompressible Navier--Stokes system concerning the physical modeling as well as regularization by noise.
Original languageEnglish
Pages (from-to)4465-4494
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Issue number4
Early online date21 Jul 2022
Publication statusPublished - 2022


  • compressible fluids
  • stochastic Navier-Stokes system
  • transport noise

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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