On endpoint regularity criterion of 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...

An Osgood Type Regularity Criterion for the 3D Boussinesq Equations

We consider the three-dimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient.

On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity, η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. As same as the 3D Navier-Stokes equations, the regularity of ...

Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity∗

In this short note, we give a link between the regularity of the solution u to the 3D Navier-Stokes equation, and the behavior of the direction of the velocity u/|u|. It is shown that the control of div(u/|u|) in a suitable Lpt (L q x) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin...

A regularity criterion of weak solutions to the 3D Boussinesq equations