Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit

Luo D, Zhu R (2021)
Stochastic Processes and their Applications 140: 236-286.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Luo, Dejun; Zhu, RongchanUniBi
Abstract / Bemerkung
We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus T-2, perturbed by multiplicative transport noise. The equation admits the white noise measure on T-2 as the invariant measure. We first prove the existence of white noise solutions to the stochastic equation via the method of point vortex approximation, then, under a suitable scaling limit of the noise, we show that the solutions converge weakly to the unique stationary solution of the dissipative mSQG equation driven by spacetime white noise. The weak uniqueness of the latter equation is also proved by following Gubinelli and Perkowski's approach in Gubinelli and Perkowski (2020). (C) 2021 Elsevier B.V. All rights reserved.
Stichworte
Modified Surface Quasi-Geostrophic equation; Transport noise; White; noise solution; Scaling limit; Weak convergence
Erscheinungsjahr
2021
Zeitschriftentitel
Stochastic Processes and their Applications
Band
140
Seite(n)
236-286
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2957360

Zitieren

Luo D, Zhu R. Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit. Stochastic Processes and their Applications. 2021;140:236-286.
Luo, D., & Zhu, R. (2021). Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit. Stochastic Processes and their Applications, 140, 236-286. https://doi.org/10.1016/j.spa.2021.06.013
Luo, D., and Zhu, R. (2021). Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit. Stochastic Processes and their Applications 140, 236-286.
Luo, D., & Zhu, R., 2021. Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit. Stochastic Processes and their Applications, 140, p 236-286.
D. Luo and R. Zhu, “Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit”, Stochastic Processes and their Applications, vol. 140, 2021, pp. 236-286.
Luo, D., Zhu, R.: Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit. Stochastic Processes and their Applications. 140, 236-286 (2021).
Luo, Dejun, and Zhu, Rongchan. “Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit”. Stochastic Processes and their Applications 140 (2021): 236-286.

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