ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES

Breit D, Feireisl E, Hofmanová M (2020)
ANALYSIS & PDE 13(2): 371-402.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Breit, Dominic; Feireisl, Eduard; Hofmanová, MartinaUniBi
Abstract / Bemerkung
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) -> infinity 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.
Stichworte
stochastic compressible Euler system; weak solution; compressible Euler; system; stochastic forcing; ill-posedness; convex integration
Erscheinungsjahr
2020
Zeitschriftentitel
ANALYSIS & PDE
Band
13
Ausgabe
2
Seite(n)
371-402
ISSN
1948-206X
Page URI
https://pub.uni-bielefeld.de/record/2942741

Zitieren

Breit D, Feireisl E, Hofmanová M. ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES. ANALYSIS & PDE. 2020;13(2):371-402.
Breit, D., Feireisl, E., & Hofmanová, M. (2020). ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES. ANALYSIS & PDE, 13(2), 371-402. doi:10.2140/apde.2020.13.371
Breit, D., Feireisl, E., and Hofmanová, M. (2020). ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES. ANALYSIS & PDE 13, 371-402.
Breit, D., Feireisl, E., & Hofmanová, M., 2020. ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES. ANALYSIS & PDE, 13(2), p 371-402.
D. Breit, E. Feireisl, and M. Hofmanová, “ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES”, ANALYSIS & PDE, vol. 13, 2020, pp. 371-402.
Breit, D., Feireisl, E., Hofmanová, M.: ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES. ANALYSIS & PDE. 13, 371-402 (2020).
Breit, Dominic, Feireisl, Eduard, and Hofmanová, Martina. “ON SOLVABILITY AND ILL-POSEDNESS OF THE COMPRESSIBLE EULER SYSTEM SUBJECT TO STOCHASTIC FORCES”. ANALYSIS & PDE 13.2 (2020): 371-402.

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