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Breit, Dominic and Hofmanova, Martina (2016): Stochastic Navier-Stokes Equations for Compressible Fluids. In: Indiana University Mathematics Journal, Vol. 65, No. 4: pp. 1183-1250

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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 exponent 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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