A Weak-L p Prodi–Serrin Type Regularity Criterion for the Navier–Stokes Equations

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.

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...

A new regularity criterion for weak solutions to the Navier-Stokes equations

In this paper we obtain a new regularity criterion for weak solutions to the 3-D Navier-Stokes equations. We show that if any one component of the velocity field belongs to L([0, T ); L(R)) with 2 α + 3 γ ≤ 1 2 , 6 < γ ≤ ∞, then the weak solution actually is regular and unique. Titre. Un nouveau critère de régularité pour les solutions faibles des équations de Navier-Stokes Resumé. Dans cet art...

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 Weak Solution to the 3D Micropolar Fluid Equations