On the result of He concerning the smoothness of solutions to the Navier-Stokes equations. (English) Zbl 1014.35073

Pokorný, Milan

Electron. J. Differ. Equ. 2003, Paper No. 11, 8 p. (2003).

Summary: We improve the regularity criterion for the Navier-Stokes equations proved by Ch. He [ibid. 2002, Paper No. 29, 13 p., electronic only (2002; Zbl 0993.35072)]. We show that for the Cauchy problem the Leray-Hopf weak solution is smooth provided \(\nabla u_3 \in L^t(0,T;L^s)\), \(\frac 2t + \frac 3s \leq \frac 32\).

MSC:

35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

Navier-Stokes equations; regularity of systems of PDE’s; anisotropic regularity criteria; Cauchy problem; Leray-Hopf weak solution

Citations:

Zbl 0993.35072