Stochastic Navier-Stokes equations for compressible fluids

Dominic Breit; Martina Hofmanová

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arXiv · 1409.2706

Stochastic Navier-Stokes equations for compressible fluids

Dominic Breit·Martina Hofmanová

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Abstract

We study the Navier-Stokes equations governing the motion of 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, which is affine linear in momentum and satisfies suitable growth assumptions with respect to density, and establish existence of the so-called finite energy weak martingale solution under the condition that the adiabatic constant satisfies $\gamma>3/2$. 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.

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Dominic Breit, Martina Hofmanová. 2014-09-09. Stochastic Navier-Stokes equations for compressible fluids. https://arxiv.org/abs/1409.2706

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