On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise
Bechtold F, Lange T, Wichmann J (2024)
Electronic Journal of Probability 29: 173.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Einrichtung
Abstract / Bemerkung
We study the surface quasi-geostrophic equation driven by a generic additive noise process W. By means of convex integration techniques, we establish existence of weak solutions whenever the stochastic convolution z associated with W is well defined and fulfills certain regularity constraints. Quintessentially, we show that the so constructed solutions to the non-linear equation are controlled by z in a linear fashion. This allows us to deduce further properties of the so constructed solutions, without relying on structural probabilistic properties such as Gaussianity, Markovianity or a martingale property of the underlying noise W.
Stichworte
SQG equation;
stochastic partial differential equations;
additive noise;
convex integration;
stochastic fluid dynamics
Erscheinungsjahr
2024
Zeitschriftentitel
Electronic Journal of Probability
Band
29
Art.-Nr.
173
Urheberrecht / Lizenzen
eISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2987289
Zitieren
Bechtold F, Lange T, Wichmann J. On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. Electronic Journal of Probability . 2024;29: 173.
Bechtold, F., Lange, T., & Wichmann, J. (2024). On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. Electronic Journal of Probability , 29, 173. https://doi.org/10.1214/24-EJP1221
Bechtold, Florian, Lange, Theresa, and Wichmann, Jörn. 2024. “On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise”. Electronic Journal of Probability 29: 173.
Bechtold, F., Lange, T., and Wichmann, J. (2024). On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. Electronic Journal of Probability 29:173.
Bechtold, F., Lange, T., & Wichmann, J., 2024. On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. Electronic Journal of Probability , 29: 173.
F. Bechtold, T. Lange, and J. Wichmann, “On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise”, Electronic Journal of Probability , vol. 29, 2024, : 173.
Bechtold, F., Lange, T., Wichmann, J.: On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. Electronic Journal of Probability . 29, : 173 (2024).
Bechtold, Florian, Lange, Theresa, and Wichmann, Jörn. “On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise”. Electronic Journal of Probability 29 (2024): 173.
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arXiv: 10.48550/ARXIV.2311.00670
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