Stochastic isentropic Euler equations

Berthelin, Florent; Vovelle, Julien

doi:10.24033/asens.2386

Stochastic isentropic Euler equations
[Équations d'Euler stochastiques isentropiques]

Berthelin, Florent ; Vovelle, Julien

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 1, pp. 181-254.

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Résumé
Abstract

Nous étudions le système d'Euler des gaz isentropiques, pour une loi de pression en $ρ^{γ}$ , avec un forçage stochastique. Nous prouvons l'existence de solutions martingales vérifiant des inégalités entropiques. Nous discutons également de l'existence et de la caractérisation de mesures invariantes dans la section de conclusion.

We study the stochastically forced system of isentropic Euler equations of gas dynamics with a $γ$ -law for the pressure. We show the existence of martingale weak entropy solutions; we also discuss the existence and characterization of invariant measures in the concluding section.

DOI : 10.24033/asens.2386

Classification : 60H15, 35R60, 35L65, 76N15.
Keywords: Stochastic partial differential equations, isentropic Euler equations, entropy solutions.
Mot clés : Équations aux dérivées partielles stochastiques, système d'Euler isentropique, solutions entropiques.

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     author = {Berthelin, Florent and Vovelle, Julien},
     title = {Stochastic isentropic {Euler} equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {181--254},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 52},
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Berthelin, Florent; Vovelle, Julien. Stochastic isentropic Euler equations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 1, pp. 181-254. doi : 10.24033/asens.2386. http://www.numdam.org/articles/10.24033/asens.2386/

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