Nonlinear Partial Differential Equations

Date: November 24, 2020

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Yanqiu Guo, Florida International University

Title: Analysis of a rapidly rotating convection model of tall columnar structure

Abstract: In geophysics, thermal convection is often influenced by planetary rotation. Coherence structures in convection under moderate rotation are exclusively cyclonic. However, for rapid rotation, experiments have revealed a transition to equal populations of cyclonic and anticyclonic structures. In order to study such interesting phenomena numerically, Sprague, Julien, Knobloch, and Werne derived a reduced system of equations for rotationally constrained convection valid in the asymptotic limit of thin columnar structures and rapid rotation. In the talk, I will introduce this convection model, and provide a global regularity result when the system is regularized by a weak dissipation. Also, I will discuss the global well-posedness of the system at infinite Prandtl and Rayleigh numbers. This is a joint project with Chongsheng Cao and Edriss Titi.