Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component. (English) Zbl 1458.35098

Zhang, Zujin

Czech. Math. J. 68, No. 1, 219-225 (2018).

Summary: We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of \(u_3\) and \(\omega_3\), which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel and M. Pokorný [Appl. Math., Praha 49, No. 5, 483–493 (2004; Zbl 1099.35101)].

MSC:

35B65	Smoothness and regularity of solutions to PDEs
35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

regularity criterion; Navier-Stokes equation

Citations:

Zbl 1099.35101