Prodi-Serrin condition for 3D Navier-Stokes equations via one directional derivative of velocity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:298

Article

Chen, Hui¹  Le, Wenjun¹  Qian, Chenyin² 

[1] Zhejiang Univ Sci & Technol, Sch Sci, Hangzhou 310023, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

关键词: Navier-Stokes equations;    Regularity of weak solutions;    Serrin-Prodi condition;   

DOI  :  10.1016/j.jde.2021.07.015

来源: Elsevier

【 摘 要 】

In this paper, we consider the conditional regularity of weak solution to the 3D Navier-Stokes equations. More precisely, we prove that if one directional derivative of velocity, say partial derivative(3)u, satisfies partial derivative(3)u is an element of L-p0,L-1 (0, T; L-q0(R-3)) with 2/p(0) + 3/q(0) = 2 and 3/2 < q(0) < +infinity, then the weak solution is regular on (0, T]. The proof is based on the new local energy estimates introduced by Chae-Wolf (2019) [4] and Wang-Wu-Zhang (2020) [21]. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free