Regularity criteria for strong solutions to the 3D Navier–Stokes equations

A study on the global regularity for a model of the 3D axisymmetric NavierStokes equations

We investigates the global regularity issue concerning a model equation proposed by Hou and Lei [3] to understand the stabilizing effects of the nonlinear terms in the 3D axisymmetric Navier-Stokes and Euler equations. Two major results are obtained. The first one establishes the global regularity of a generalized version of their model with a fractional Laplacian when the fractional power sati...

Two regularity criteria for the 3D MHD equations

This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one-direction while the second one requires suitable boundedness of the derivative of the pressure in one-direction.

Remarks on Regularity Criteria for the 3d Navier-stokes Equations

In this article, we study the regularity criteria for the 3D NavierStokes equations involving derivatives of the partial components of the velocity. It is proved that if ∇he u belongs to Triebel-Lizorkin space, ∇u3 or u3 belongs to Morrey-Campanato space, then the solution remains smooth on [0, T ].

Regularity Criteria Involving the Pressure for the Weak Solutions to the Navier-stokes Equations

In this paper we consider the Cauchy problem for the n-dimensional Navier-Stokes equations and we prove a regularity criterion for weak solutions involving the summability of the pressure. Related results for the initial-boundary value problem are also presented.

Regularity Criteria for the Generalized MHD Equations