On the critical one-component velocity regularity criteria to 3-D incompressible MHD system

Regularity Criteria of the Three-dimensional Mhd System Involving One Velocity and One Vorticity Component

We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four nonlinear terms making u...

Global Small Solutions to 2-d Incompressible Mhd System

In this paper, we consider the global wellposedness of 2-D incompressible magnetohydrodynamical system with small and smooth initial data. It is a coupled system between the Navier-Stokes equations and a free transport equation with an universal nonlinear coupling structure. The main difficulty of the proof lies in exploring the dissipative mechanism of the system due to the fact that there is ...

Regularity Criteria for the Generalized MHD Equations

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.

On estimating 3-D incompressible motion

In this paper we present a new method for estimating the 3-D motion of an incompressible or nearly incompressible body from a set noisy and possibly sparse measurements. This problem occurs in applications such as the estimation of heart motion and uid ow. Our method is based on a stochastic motion model where the incompressibility condition is modeled as a correlation between certain component...