### Abstract

We study the Navier-Stokes equations governing the motion of an isentropic
compressible
fluid in three dimensions driven by a multiplicative stochastic forcing. In
particular, we consider a stochastic perturbation of the system as a function of momentum
and density. We establish existence of a so-called finite energy weak martingale solution
under the condition that the adiabatic constant satisfies γ> 3/2. The proof is based on
a four layer approximation scheme together with a refined stochastic compactness method
and a careful identification of the limit procedure.

Original language | English |
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Pages (from-to) | 1183–1250 |

Number of pages | 68 |

Journal | Indiana University Mathematics Journal |

Volume | 65 |

Issue number | 4 |

Publication status | Published - 2016 |

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## Cite this

Breit, D., & Hofmanova, M. (2016). Stochastic Navier-Stokes equations for compressible fluids.

*Indiana University Mathematics Journal*,*65*(4), 1183–1250. http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=5832&year=2016&volume=65