A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA

Röckner M, Zhu R, Zhu X (2019)
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 24(8): 4021-4030.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper, we prove that the solution constructed in [2] satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in [x]. As a result, we obtain the existence and uniqueness of the global solutions to the stochastic vorticity equations in 3D case for the small initial data independent of time, which can be viewed as a stochastic version of the Kato-Fujita result (see [10]).
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Zeitschriftentitel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Band
24
Ausgabe
8
Seite(n)
4021-4030
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Röckner M, Zhu R, Zhu X. A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 2019;24(8):4021-4030.
Röckner, M., Zhu, R., & Zhu, X. (2019). A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 24(8), 4021-4030. doi:10.3934/dcdsb.2019048
Röckner, M., Zhu, R., and Zhu, X. (2019). A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 24, 4021-4030.
Röckner, M., Zhu, R., & Zhu, X., 2019. A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 24(8), p 4021-4030.
M. Röckner, R. Zhu, and X. Zhu, “A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA”, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 24, 2019, pp. 4021-4030.
Röckner, M., Zhu, R., Zhu, X.: A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 24, 4021-4030 (2019).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “A REMARK ON GLOBAL SOLUTIONS TO RANDOM 3D VORTICITY EQUATIONS FOR SMALL INITIAL DATA”. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 24.8 (2019): 4021-4030.