On solvability and ill-posedness of the compressible Euler system subject to stochastic forces

By Dominic Breit, Eduard Feireisl, Martina Hofmanov'a. 2017

49 citations recorded by the source corpus.

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 $\tau_M \to \infty$ 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 {\it a priori} given stochastic basis and adapted to the driving stochastic process.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/3f9387bbf011b71bf0e772a362ad04f2261a420c

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In Applied Mathematics

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a

In Computational Mechanics

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a

In Finance

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a
4. Panagiotis E. Souganidis

Citations in the corpus

• On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations (2020, methodology): “The first application of this method in the stochastic setting was done in [6].”