Global Well-posedness of the 3D Primitive Equations With Partial Vertical Turbulence Mixing Heat Diffusion

摘要

The three--dimensional incompressible viscous Boussinesq equations, under theassumption of hydrostatic balance, govern the large scale dynamics ofatmospheric and oceanic motion, and are commonly called the primitiveequations. To overcome the turbulence mixing a partial vertical diffusion isusually added to the temperature advection (or density stratification)equation. In this paper we prove the global regularity of strong solutions tothis model in a three-dimensional infinite horizontal channel, subject toperiodic boundary conditions in the horizontal directions, and withno-penetration and stress-free boundary conditions on the solid, top andbottom, boundaries. Specifically, we show that short time strong solutions tothe above problem exist globally in time, and that they depend continuously onthe initial data.