On the smoothness of a class of weak solutions to the Navier-Stokes equations. (English) Zbl 0972.35089

Beirão da Veiga, Hugo

J. Math. Fluid Mech. 2, No. 4, 315-323 (2000).

Using an improved square integrability criterion, where the velocity \(u\) is replaced by its projection \(\overline u\) onto an arbitrary hyperplane in \(\mathbb{R}^n\), \(n\leq 4\), the author establishes regularity of a class of weak solutions to the nonstationary Navier-Stokes equations.

Reviewer: Oleg Titow (Berlin)

MSC:

35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B65	Smoothness and regularity of solutions to PDEs
35D30	Weak solutions to PDEs

Keywords:

regularity criterion; square integrability criterion; velocity; projection; hyperplane; weak solutions; nonstationary Navier-Stokes equations