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On solvability and
ill-posedness of the compressible Euler system subject to
stochastic forces
Dominic Breit, Eduard Feireisl and Martina Hofmanová |
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Vol. 13 (2020), No. 2, 371–402
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Abstract |
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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 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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Keywords
stochastic compressible Euler system, weak solution,
compressible Euler system, stochastic forcing,
ill-posedness, convex integration
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Mathematical Subject Classification 2010
Primary: 35Q31
Secondary: 35D30, 60H15
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Milestones
Received: 24 May 2017
Revised: 8 December 2018
Accepted: 23 February 2019
Published: 19 March 2020
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Authors |
| Dominic Breit | |
| Department of Mathematics Heriot-Watt University Edinburgh United Kingdom |
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| Eduard Feireisl | |
| Institute of Mathematics Academy of Sciences of the Czech Republic Prague Czech Republic |
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| Martina Hofmanová | |
| Technical University Berlin Institute of Mathematics Berlin Germany |
Fakultät für Mathematik Universität Bielefeld Bielefeld Germany |
