A remark on global solutions to random 3D vorticity equations for small initial data

Michael Röckner; Rongchan Zhu; Xiangchan Zhu

doi:10.3934/dcdsb.2019048

A remark on global solutions to random 3D vorticity equations for small initial data

Michael Röckner
, Rongchan Zhu
, Xiangchan Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Bielefeld University
Beijing Jiaotong University
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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 [8]. 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]).

Original language	English
Pages (from-to)	4021-4030
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	24
Issue number	8
DOIs	https://doi.org/10.3934/dcdsb.2019048
Publication status	Published - Aug 2019

Keywords

Controlled rough path
Small initial data
Stochastic vorticity equations

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10.3934/dcdsb.2019048

Cite this

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abstract = "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 [8]. 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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author = "Michael R{\"o}ckner and Rongchan Zhu and Xiangchan Zhu",

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AU - Röckner, Michael

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

PY - 2019/8

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N2 - 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 [8]. 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]).

AB - 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 [8]. 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]).

KW - Controlled rough path

KW - Small initial data

KW - Stochastic vorticity equations

UR - https://www.scopus.com/pages/publications/85072556278

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DO - 10.3934/dcdsb.2019048

M3 - Article

AN - SCOPUS:85072556278

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VL - 24

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 8

ER -

A remark on global solutions to random 3D vorticity equations for small initial data

Abstract

Keywords

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