2016/06/17 by Dominic Breit, Eduard Feireisl, Breit, Dominic +4
Economics, Econometrics and Finance · Engineering · Mathematics · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP
paper · pdf · doi:10.48550/arxiv.1606.05441
arxiv created 2016/06/17 · arxiv updated 2016/06/20
We study the Navier-Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence (up to a positive stopping time) of a unique solution, which is strong in both PDE and probabilistic sense. Our approach relies on rewriting the problem as a symmetric hyperbolic system augmented by partial diffusion, which is solved via a suitable approximation procedure using the stochastic compactness method and the Yamada-Watanabe type argument based on the Gyöngy-Krylov characterization of convergence in probability. This leads to the existence of a strong (in the PDE sense) pathwise solution. Finally, we use various stopping time arguments to establish the local existence of a unique strong solution to the original problem.