To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:



Large scale dynamics of the oceans and the atmosphere are commonly governed by the primitive equations (PEs), also known as Hydrostatic Euler Equations. While it is by now well-known that the 3D viscous primitive equations are globally well-posed in Sobolev spaces, my talk will solely focus on the invisicd case. First, I will briefly discuss the ill posedness in Sobolev spaces, the local well-posedness in the space of analytic functions, and finite-time blowup of solution to the 3D inviscid PEs with rotation (Coriolis force). Then I will also show, in the case of “well-prepared” analytic initial data, the regularizing effect of the Coriolis force by providing a lower bound for the life-span of the solutions that grows toward infinity with the rotation rate. These are joint works with T. E. Ghoul, Q. Lin and E. S. Titi.

Effect of the Rotation on the Inviscid Primitive Equations for Planetary Geophysical Flows