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2020 On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
Dominic Breit, Eduard Feireisl, Martina Hofmanová
Anal. PDE 13(2): 371-402 (2020). DOI: 10.2140/apde.2020.13.371

Abstract

We consider the barotropic Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of weak (distributional) solutions. Specifically, we find a sequence τM of positive stopping times for which the Euler system admits infinitely many solutions originating from the same initial data. The solutions are weak in the PDE sense but strong in the probabilistic sense, meaning, they are defined on an a priori given stochastic basis and adapted to the driving stochastic process.

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Dominic Breit. Eduard Feireisl. Martina Hofmanová. "On solvability and ill-posedness of the compressible Euler system subject to stochastic forces." Anal. PDE 13 (2) 371 - 402, 2020. https://doi.org/10.2140/apde.2020.13.371

Information

Received: 24 May 2017; Revised: 8 December 2018; Accepted: 23 February 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07181504
MathSciNet: MR4078230
Digital Object Identifier: 10.2140/apde.2020.13.371

Subjects:
Primary: 35Q31
Secondary: 35D30 , 60H15

Keywords: compressible Euler system , convex integration , ill-posedness , stochastic compressible Euler system , stochastic forcing , Weak solution

Rights: Copyright © 2020 Mathematical Sciences Publishers

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