A Regularity Criterion for the Navier-Stokes Equations in Terms of One Directional Derivative of the Velocity

作者：Liu, Qiao^*

来源：Acta Applicandae Mathematicae, 2015, 140(1): 1-9.

DOI：10.1007/s10440-014-9975-z

• Navier-Stokes equations
• Regularity
• Weak solution
• Morrey-Campanato space

We consider the regularity criterion for the three dimensional incompressible Navier-Stokes equations in terms of one directional derivative of the velocity. The result shows that if weak solution u satisfies
partial derivative(3)u is an element of L2/1-r (0, T; (M) Over dot(p,3/r) (R-3)) with 0 < r < 1 and 2 <= p <= 3/r, then u is regular on (0, T] x R-3. Here, is the homogeneous Morrey-Campanato space.

• 出版日期2015-12
• 单位湖南师范大学