Please join us welcoming Edriss Titi, University of Cambridge, Texas A&M and Weizmann Institute of Science. Professor Titi will be talking on the The Inviscid Primitive Equations and the Effect of Rotation.

Abstract Large scale dynamics of the oceans and the atmosphere are governed by the primitive equation (PE). It is well-known that the three-dimensional viscous PE is globally well-posed in Sobolev spaces. In this talk, I will discuss the ill-posedness in Sobolev spaces, the local well-posedness in the space of analytic functions, and the finite-time blowup of solutions to the three-dimensional inviscid PE (also known as the hydrostatic Euler equations) with rotation (Coriolis force). Eventually, 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 which grows toward infinity with the rotation rate. The latter is achieved by a delicate analysis of a simple limit resonant system whose solution approximates the corresponding solution of the 3D inviscid PE  with the same initial data. In addition, I will discuss the Onsager conjecture in the context of the inviscid primitive equations.

Graduate Students are encouraged to attend.