An Osgood Type Regularity Criterion for the 3D Boussinesq Equations

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

GLOBAL REGULARITY CRITERIA FOR THE n-DIMENSIONAL BOUSSINESQ EQUATIONS WITH FRACTIONAL DISSIPATION

We consider the n-dimensional Boussinesq equations with fractional dissipation, and establish a regularity criterion in terms of the velocity gradient in Besov spaces with negative order.

Global Well-posedness for the 2d Boussinesq System without Heat Diffusion and with Either Anisotropic Viscosity or Inviscid Voigt-α Regularization

We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. Although we follow some of their...

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 ...

On the Regularity of Three-Dimensional Rotating Euler-Boussinesq Equations

The 3D rotating Boussinesq equations (the \primitive" equations of geophysical uid ows) are analyzed in the asymptotic limit of strong stable stratiication. The resolution of resonances and a non-standard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on innnite time intervals of regular solutions to the viscous 3D \primitive" equati...