乘子空间中广义Navier-Stokes方程弱解的正则性准则(英文)

Regularity Criteria for the 3D Generalized Navier-Stokes Equations in Terms of Two Velocity Components

利用能量估计与不等式研究三维广义Navier-Stokes方程弱解的正则性准则,证明如果速度场的水平分量ū=(u1,u2,0)满足ū∈L2α-(r+1)2α(0,T;r),r∈[0,1),或者水平速度场的水平梯度▽hū=(α1ū,α2ū)满足▽hū∈L2α-r2α(0,T;r),r∈[0,1],则弱解在[0,T)是唯一的强解.

In this paper,we consider the regularity for weak solutions to the generalized NavierStokes equations in R3.It is proved that if the horizontal velocityū=（u1,u2,0）satisfiesū∈L2α-（r＋1）2α（0,T;r）,r∈ [0,1）,or the horizontal gradient▽hū=（α1ū,α2ū）satisfies▽hū∈L2α-r2α（0,T;r）,r∈ [0,1],then the weak solution is actually the unique strong solution on[0,T）.