广义Navier-Stokes方程弱解的正则性准则

Regularity Criteria for Weak Solutions to the 3DGeneralized Navier-Stokes Equations

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:或者水平速度场的水平梯度▽hū=(1ū,2ū)满足:则弱解在[0,T)是唯一的强解.

In this paper,we consider regularity criteria for weak solutions to the 3D gen- eralized Navier-Stokes equations. By energy estimate and inequalities,we proved that if hori- zontal velocity u= （u1 ,u2,0） satisfies or horizontal gradient △hu=（δ1u,δ2u） satisfiesthen the weak solution is actually the unique strong solution on [0, T）.