49 research outputs found
Global Well-posedness of the 3D Primitive Equations With Partial Vertical Turbulence Mixing Heat Diffusion
The three--dimensional incompressible viscous Boussinesq equations, under the
assumption of hydrostatic balance, govern the large scale dynamics of
atmospheric and oceanic motion, and are commonly called the primitive
equations. To overcome the turbulence mixing a partial vertical diffusion is
usually added to the temperature advection (or density stratification)
equation. In this paper we prove the global regularity of strong solutions to
this model in a three-dimensional infinite horizontal channel, subject to
periodic boundary conditions in the horizontal directions, and with
no-penetration and stress-free boundary conditions on the solid, top and
bottom, boundaries. Specifically, we show that short time strong solutions to
the above problem exist globally in time, and that they depend continuously on
the initial data
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
Pressure Regularity Criterion for the Three-dimensional Navier-Stokes Equations in Infinite Channel
In this paper we consider the three-dimensional Navier-Stokes equations in an
infinite channel. We provide a sufficient condition, in terms of , where is the pressure, for the global existence of the strong solutions
to the three-dimensional Navier-Stokes equations
Global Regularity for an Inviscid Three-dimensional Slow Limiting Ocean Dynamics Model
We establish, for smooth enough initial data, the global well-posedness
(existence, uniqueness and continuous dependence on initial data) of solutions,
for an inviscid three-dimensional {\it slow limiting ocean dynamics} model.
This model was derived as a strong rotation limit of the rotating and
stratified Boussinesg equations with periodic boundary conditions. To establish
our results we utilize the tools developed for investigating the
two-dimensional incompressible Euler equations and linear transport equations.
Using a weaker formulation of the model we also show the global existence and
uniqueness of solutions, for less regular initial data
Strong solutions to the 3D primitive equations with only horizontal dissipation: near initial data
In this paper, we consider the initial-boundary value problem of the
three-dimensional primitive equations for oceanic and atmospheric dynamics with
only horizontal viscosity and horizontal diffusivity. We establish the local,
in time, well-posedness of strong solutions, for any initial data , by using the local, in space, type energy estimate. We also
establish the global well-posedness of strong solutions for this system, with
any initial data , such that , for some , by using the logarithmic type anisotropic
Sobolev inequality and a logarithmic type Gronwall inequality. This paper
improves the previous results obtained in [Cao, C.; Li, J.; Titi, E.S.: Global
well-posedness of the 3D primitive equations with only horizontal viscosity and
diffusivity, Comm. Pure Appl.Math., Vol. 69 (2016), 1492-1531.], where the
initial data was assumed to have regularity
Local and Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
In this paper, we consider the initial-boundary value problem of the viscous
3D primitive equations for oceanic and atmospheric dynamics with only vertical
diffusion in the temperature equation. Local and global well-posedness of
strong solutions are established for this system with initial data