Events for 09/15/2020 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Quyuan Lin, Texas A&M University

Title: Three-dimensional Inviscid Primitive Equations with 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 finite-time blowup of solution to the three-dimensional inviscid PEs with rotation (Coriolis force). Moreover, 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. Joint work with Tej Ghoul, Slim Ibrahim and Edriss S. Titi