压力项属于Triebel-Lizorkin空间的三维不可压Navier-Stokes方程的正则性准则  

Regularity Criterion for 3D Incompressible Navier-Stokes Equations via the Pressure in Triebel-Lizorkin Spaces

作　　者：万雅琪 陈晓莉 Yaqi Wan;Xiaoli Chen(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022)

机构地区：[1]江西师范大学数学与统计学院,南昌330022

出　　处：《数学物理学报（A辑）》2022年第5期1473-1481,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971209,11961032);江西省教育厅基金。

摘　　要：该文研究了R^(3)中的Navier-Stokes方程弱解的正则性准则,证明了当π∈Lp(0,T;F˙0q,10q/5q+6(R^(3)))时Leray-Hopf弱解u是正则的,其中2/p+3/q<7/4,12/5<q≤∞同时还证明了当∇π∈Lp(0,T;F˙0q,8q/12−3/q(R^(3)))时,弱解u能光滑的延拓出t=T,其中2/p+3/q=114,12/11<q<4.In this paper,we consider the regularity criterion of weak solution to Navier-Stokes equations in R^(3).It is proved that a Leray-Hopf weak solution u becomes a regular solution if the pressureπ∈Lp(0,T;F˙0q,10q/5q+6(R^(3)))with 2/p+3/q<7/4,12/5<q≤∞.Meanwhile the authors also prove that if the gradient of the pressure∇π∈Lp(0,T;F˙0q,8q/12−3/q(R^(3)))with 2/p+3/q=114,12/11<q<4,then the weak solution u can be smoothly extended beyond t=T.

关 键 词：NAVIER-STOKES方程 爆破判别准则 Leray-Hopf弱解 TRIEBEL-LIZORKIN空间 压力 

分 类 号：O175.26[理学—数学]