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.
|Number of pages||68|
|Journal||Indiana University Mathematics Journal|
|Publication status||Published - 2016|
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