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^*

^*此作品的通讯作者

数学学院

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

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

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]).

源语言	英语
页（从-至）	4021-4030
页数	10
期刊	Discrete and Continuous Dynamical Systems - Series B
卷	24
期	8
DOI	https://doi.org/10.3934/dcdsb.2019048
出版状态	已出版 - 8月 2019

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title = "A remark on global solutions to random 3D vorticity equations for small initial data",

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]).",

keywords = "Controlled rough path, Small initial data, Stochastic vorticity equations",

author = "Michael R{\"o}ckner and Rongchan Zhu and Xiangchan Zhu",

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AU - Röckner, Michael

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

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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

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DO - 10.3934/dcdsb.2019048

M3 - Article

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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

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