The stochastic three-dimensional compressible Navier-Stokes equations are considered in a bounded domain with multiplicative noise. The global existence of martingale solution is established through the Galerkin approximation method, stopping time, compactness method and the Jakubowski-Skorokhod theorem. A martingale solution is a weak solution for the fluid variables and the Brownian motion on a probability space. The initial data is arbitrarily large and satisfies a natural compatibility condition.
"Global existence of martingale solutions to the three-dimensional stochastic compressible Navier-Stokes equations." Differential Integral Equations 28 (11/12) 1105 - 1154, November/December 2015. https://doi.org/10.57262/die/1439901044