On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations

Hofmanová M, Zhu R, Zhu X (2021)
Communications on Pure and Applied Mathematics .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Abstract / Bemerkung
We are concerned with the question of well-posedness of stochastic, three-dimensional, incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak-strong uniqueness; (iii) nonuniqueness in law; (iv) existence of a strong Markov solution; (v) nonuniqueness of strong Markov solutions: all hold true within this class. Moreover, as a by-product of (iii) we obtain existence and nonuniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality. (c) 2021 Wiley Periodicals LLC.
Erscheinungsjahr
2021
Zeitschriftentitel
Communications on Pure and Applied Mathematics
ISSN
0010-3640
eISSN
1097-0312
Page URI
https://pub.uni-bielefeld.de/record/2958499

Zitieren

Hofmanová M, Zhu R, Zhu X. On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations. Communications on Pure and Applied Mathematics . 2021.
Hofmanová, M., Zhu, R., & Zhu, X. (2021). On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations. Communications on Pure and Applied Mathematics . https://doi.org/10.1002/cpa.22023
Hofmanová, M., Zhu, R., and Zhu, X. (2021). On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations. Communications on Pure and Applied Mathematics .
Hofmanová, M., Zhu, R., & Zhu, X., 2021. On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations. Communications on Pure and Applied Mathematics .
M. Hofmanová, R. Zhu, and X. Zhu, “On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations”, Communications on Pure and Applied Mathematics , 2021.
Hofmanová, M., Zhu, R., Zhu, X.: On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations. Communications on Pure and Applied Mathematics . (2021).
Hofmanová, Martina, Zhu, Rongchan, and Zhu, Xiangchan. “On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations”. Communications on Pure and Applied Mathematics (2021).

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