The Inviscid Primitive Equations and the Effect of Rotation

Abstract: Large scale dynamics of the oceans and the atmosphere is governed by the primitive equations (PEs). It is well-known that the three-dimensional viscous primitive equations are 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 PEs 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 approximate the corresponding solution of the 3D inviscid PEs with the same initial data.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

"Partial Differential Equations and Applications" Webinar