On Wolf's Regularity Criterion of Suitable Weak Solutions to the Navier-Stokes Equations

被引:9
作者
Jiu, Quansen [1 ]
Wang, Yanqing [2 ]
Zhou, Daoguo [3 ]
机构
[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[2] Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China
[3] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China
基金
北京市自然科学基金; 中国国家自然科学基金;
关键词
Navier-Stokes equations; Suitable weak solutions; Regularity;
D O I
10.1007/s00021-019-0426-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier-Stokes equations. By means of the local pressure projection introduced by Wolf (in: Rannacher, Sequeira (eds) Advances in mathematical fluid mechanics, Springer, Berlin, 2010, Ann Univ Ferrara 61: 149-171, 2015), we establish a Caccioppoli type inequality just in terms of velocity field for suitable weak solutions to this system 2 L 20 7, 15 4 Q(12) + . u 2 L2(Q(12)) = C u 2 L 20 7 (Q(1)) + C u 4 L 20 7 (Q(1)). This allows us to derive a new e-regularity criterion: Let u be a suitable weak solution in the Navier-Stokes equations. There exists an absolute positive constant e such that if u satisfies Q(1) | u| 20/ 7dxdt e, then u is bounded in some neighborhood of point (0, 0). This gives an improvement of previous corresponding results obtained in Chae and Wolf (Arch Ration Mech Anal 225: 549-572, 2017), in Guevara and Phuc (Calc Var 56: 68, 2017) and Wolf (Ann Univ Ferrara 61: 149-171, 2015).
引用
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页数:16
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