Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise

Hofmanová M, Lange T, Pappalettera U (2024)
Probability Theory and Related Fields 188: 1183–1255.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We construct Holder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Holder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow transformation reducing the SPDE under investigation to a random PDE, and convex integration techniques introduced in the deterministic setting by De Lellis and Szekelyhidi, here adapted to consider the stochastic case. In particular, our novel approach allows to construct probabilistically strong solutions on [0,infinity) directly.
Stichworte
Fluid dynamics; Euler equations; Transport noise; Convex integration
Erscheinungsjahr
2024
Zeitschriftentitel
Probability Theory and Related Fields
Band
188
Seite(n)
1183–1255
ISSN
0178-8051
eISSN
1432-2064
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2985884

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Hofmanová M, Lange T, Pappalettera U. Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise. Probability Theory and Related Fields. 2024;188:1183–1255.
Hofmanová, M., Lange, T., & Pappalettera, U. (2024). Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise. Probability Theory and Related Fields, 188, 1183–1255. https://doi.org/10.1007/s00440-023-01233-5
Hofmanová, Martina, Lange, Theresa, and Pappalettera, Umberto. 2024. “Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise”. Probability Theory and Related Fields 188: 1183–1255.
Hofmanová, M., Lange, T., and Pappalettera, U. (2024). Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise. Probability Theory and Related Fields 188, 1183–1255.
Hofmanová, M., Lange, T., & Pappalettera, U., 2024. Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise. Probability Theory and Related Fields, 188, p 1183–1255.
M. Hofmanová, T. Lange, and U. Pappalettera, “Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise”, Probability Theory and Related Fields, vol. 188, 2024, pp. 1183–1255.
Hofmanová, M., Lange, T., Pappalettera, U.: Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise. Probability Theory and Related Fields. 188, 1183–1255 (2024).
Hofmanová, Martina, Lange, Theresa, and Pappalettera, Umberto. “Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise”. Probability Theory and Related Fields 188 (2024): 1183–1255.
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2024-07-02T09:24:46Z
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