0488523 - MÚ 2019 RIV US eng J - Journal Article
Breit, D. - Feireisl, Eduard - Hofmanová, M.
Local strong solutions to the stochastic compressible Navier-Stokes system.
Communications in Partial Differential Equations. Roč. 43, č. 2 (2018), s. 313-345. ISSN 0360-5302. E-ISSN 1532-4133
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : compressible fluids * local strong solutions * Navier-Stokes system
OECD category: Pure mathematics
Impact factor: 1.239, year: 2018 ; AIS: 1.815, rok: 2018
Result website:
https://www.tandfonline.com/doi/full/10.1080/03605302.2018.1442476DOI: https://doi.org/10.1080/03605302.2018.1442476

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.
Permanent Link: http://hdl.handle.net/11104/0283105