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

被引：7

作者：

Liang, Siyu ^{[1
,2
,4
]}

Zhang, Ping ^{[1
,2
]}

Zhu, Rongchan ^{[3
,4
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[4] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 275卷

关键词：

D O I：

10.1016/j.jde.2020.11.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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) over tilde (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. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：473 / 508

页数：36

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