an:05590722
Zbl 1166.35359
Zhou, Yong
A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component
EN
Methods Appl. Anal. 9, No. 4, 563-578 (2002).
00107787
2002
j
35Q30 35B65 76D03 76D05
Summary: We consider the regularity criteria for the weak solutions to the Navier-Stokes equations in \(\mathbb{R}^3\). It is proved that if the gradient of any one component of the velocity field belongs to \(L^{\alpha,\gamma}\) with \(2/\alpha + 3/\gamma = 3/2\), \(3\leq\gamma < \infty\), then the weak solution actually is strong.