Local strong solutions to the stochastic compressible Navier-Stokes system

Dominic Breit, Eduard Feireisl, Martina Hofmanová

Research output: Contribution to journalArticle

7 Citations (Scopus)
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Abstract

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. We use 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.
Original languageEnglish
Pages (from-to)313-345
Number of pages33
JournalCommunications in Partial Differential Equations
Volume43
Issue number2
DOIs
Publication statusPublished - 8 Mar 2018

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