Sub and supercritical stochastic quasi-geostrophic equation

Röckner M, Zhu R, Zhu X (2015)
The Annals of Probability 43(3): 1202-1273.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Zhu, Rongchan; Zhu, Xiangchan
Abstract / Bemerkung
In this paper, we study the 2D stochastic quasi-geostrophic equation on T-2 for general parameter alpha epsilon (0, 1) and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise for all alpha epsilon (0, 1). In the subcritical case alpha > 1/2, we prove existence and uniqueness of (probabilistically) strong solutions. Moreover, we prove ergodicity for the solution of the stochastic quasi-geostrophic equations in the subcritical case driven by possibly degenerate noise. The law of large numbers for the solution of the stochastic quasi-geostrophic equations in the subcritical case is also established. In the case of nondegenerate noise and alpha > 2/3 in addition exponential ergodicity is proved.
Stichworte
Stochastic quasi-geostrophic equation; martingale; well posedness; problem; Markov property; strong Feller property; Markov selections; degenerate noise; ergodicity for the subcritical case
Erscheinungsjahr
2015
Zeitschriftentitel
The Annals of Probability
Band
43
Ausgabe
3
Seite(n)
1202-1273
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2759912

Zitieren

Röckner M, Zhu R, Zhu X. Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability. 2015;43(3):1202-1273.
Röckner, M., Zhu, R., & Zhu, X. (2015). Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability, 43(3), 1202-1273. doi:10.1214/13-AOP887
Röckner, M., Zhu, R., and Zhu, X. (2015). Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability 43, 1202-1273.
Röckner, M., Zhu, R., & Zhu, X., 2015. Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability, 43(3), p 1202-1273.
M. Röckner, R. Zhu, and X. Zhu, “Sub and supercritical stochastic quasi-geostrophic equation”, The Annals of Probability, vol. 43, 2015, pp. 1202-1273.
Röckner, M., Zhu, R., Zhu, X.: Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability. 43, 1202-1273 (2015).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “Sub and supercritical stochastic quasi-geostrophic equation”. The Annals of Probability 43.3 (2015): 1202-1273.

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