Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Siyu Liang; Ping Zhang; Rongchan Zhu

doi:10.1016/j.jde.2020.11.028

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Siyu Liang, Ping Zhang, Rongchan Zhu^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜^0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

源语言	英语
页（从-至）	473-508
页数	36
期刊	Journal of Differential Equations
卷	275
DOI	https://doi.org/10.1016/j.jde.2020.11.028
出版状态	已出版 - 25 2月 2021

访问文件

10.1016/j.jde.2020.11.028

其它文件与链接

链接到 Scopus 的出版物

引用此

Liang, S., Zhang, P., & Zhu, R. (2021). Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. Journal of Differential Equations, 275, 473-508. https://doi.org/10.1016/j.jde.2020.11.028

@article{dda4fe1f13964f2885c34666aba2bcb5,

title = "Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity",

abstract = "In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.",

author = "Siyu Liang and Ping Zhang and Rongchan Zhu",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = feb,

day = "25",

doi = "10.1016/j.jde.2020.11.028",

language = "English",

volume = "275",

pages = "473--508",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

AU - Liang, Siyu

AU - Zhang, Ping

AU - Zhu, Rongchan

PY - 2021/2/25

Y1 - 2021/2/25

N2 - In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

AB - In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

UR - http://www.scopus.com/inward/record.url?scp=85096880714&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2020.11.028

DO - 10.1016/j.jde.2020.11.028

M3 - Article

AN - SCOPUS:85096880714

SN - 0022-0396

VL - 275

SP - 473

EP - 508

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

摘要

访问文件

其它文件与链接

指纹

引用此