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Local strong solutions to the stochastic compressible Navier-Stokes system
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SYSNO ASEP 0488523 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Local strong solutions to the stochastic compressible Navier-Stokes system Author(s) Breit, D. (GB)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Hofmanová, M. (DE)Source Title Communications in Partial Differential Equations. - : Taylor & Francis - ISSN 0360-5302
Roč. 43, č. 2 (2018), s. 313-345Number of pages 33 s. Language eng - English Country US - United States Keywords compressible fluids ; local strong solutions ; Navier-Stokes system Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000428244800005 EID SCOPUS 85043310892 DOI https://doi.org/10.1080/03605302.2018.1442476 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
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