Local strong solutions to the stochastic compressible Navier-Stokes system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00488523" target="_blank" >RIV/67985840:_____/18:00488523 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/03605302.2018.1442476" target="_blank" >http://dx.doi.org/10.1080/03605302.2018.1442476</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03605302.2018.1442476" target="_blank" >10.1080/03605302.2018.1442476</a>

Result language
angličtina
Original language name
Local strong solutions to the stochastic compressible Navier-Stokes system
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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