The 3D Quasi-geostrophic equation: existence of solutions, lateral boundary conditions and regularity

The 3D Quasi-geostrophic equation: existence of solutions, lateral boundary conditions and regularity

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Alexis Vasseur, UT Austin
Fine Hall 314

Abstract: The 3D Quasi-geostropic equation is a model used in climatology to model the evolution of the atmosphere for small Rossby numbers. It can be derived from the primitive equation. The surface quasi-geostrophic equation  (SQG) is a special case where the atmosphere above the earth is at rest. The evolution then depends only on the boundary condition, and can be reduced to a 2D model.  

In this talk, we will show how we can derive the physical lateral boundary conditions for the inviscid 3D QG, and construct global in time weak solutions. Finally, we will discuss the global regularity of solutions to the QG equation with Ekman pumping.