Abstract

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.

Keywords

  1. compressible fluids
  2. stochastic Navier--Stokes system
  3. transport noise

MSC codes

  1. 60H15
  2. 35R60
  3. 76N10
  4. 35Q35

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 4465 - 4494
ISSN (online): 1095-7154

History

Submitted: 13 December 2021
Accepted: 5 April 2022
Published online: 21 July 2022

Keywords

  1. compressible fluids
  2. stochastic Navier--Stokes system
  3. transport noise

MSC codes

  1. 60H15
  2. 35R60
  3. 76N10
  4. 35Q35

Authors

Affiliations

Funding Information

Institute of Mathematics of the Academy of Sciences of the Czech Republic : RVO:67985840
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : SFB1283
H2020 European Research Council https://doi.org/10.13039/100010663 : 949981
Grantová Agentura České Republiky https://doi.org/10.13039/501100001824 : 21-02411S
Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/V000586/1

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