Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00506253" target="_blank" >RIV/67985840:_____/19:00506253 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/19:10402881

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00440-018-0875-4" target="_blank" >http://dx.doi.org/10.1007/s00440-018-0875-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00440-018-0875-4" target="_blank" >10.1007/s00440-018-0875-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces

Popis výsledku v původním jazyce

We study the long-time behavior of solutions to a stochastically driven Navier–Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue–Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. An essential tool in order to obtain the global-in-time estimate is the stationarity of solutions on each approximation level, which provides a certain regularizing effect. In contrast with the deterministic case, where related results were obtained only under rather restrictive constitutive assumptions for the pressure, the stochastic case is tractable in the full range of constitutive relations allowed by the available existence theory, due to the underlying martingale structure of the noise.

Název v anglickém jazyce

Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces

Popis výsledku anglicky

We study the long-time behavior of solutions to a stochastically driven Navier–Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue–Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. An essential tool in order to obtain the global-in-time estimate is the stationarity of solutions on each approximation level, which provides a certain regularizing effect. In contrast with the deterministic case, where related results were obtained only under rather restrictive constitutive assumptions for the pressure, the stochastic case is tractable in the full range of constitutive relations allowed by the available existence theory, due to the underlying martingale structure of the noise.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-08819S" target="_blank" >GA15-08819S: Stochastické procesy v nekonečně rozměrných prostorech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Probability Theory and Related Fields

ISSN

0178-8051

e-ISSN

—

Svazek periodika

174

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

52

Strana od-do

981-1032

Kód UT WoS článku

000475710400008

EID výsledku v databázi Scopus

2-s2.0-85054549818