A REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS IN TERMS OF ONE DIRECTIONAL DERIVATIVE OF THE VELOCITY FIELD

作者：Guo Zhengguang^*; Gala Sadek

来源：Analysis and Applications, 2012, 10(4): 373-380.

DOI：10.1142/S0219530512500182

• Navier-Stokes equations
• regularity criterion
• a priori estimates

We consider the regularity criterion for the incompressible Navier- Stokes equations. We show that the weak solution is regular, provided.
partial derivative u/partial derivative u is an element of L2/1 - r(0, T; X-r (R-3)) with 0 <= r <= 1
for some T > 0, where X-r is the multiplier space. This extends a result of Kukavica and Ziane [14].

• 出版日期2012-10
• 单位温州大学