Analysis of a rotationally constrained convection model
报告题目(Title)：Analysis of a rotationally constrained convection model
报告人(Speaker)：Edriss S. Titi（University of Cambridge, The Weizmann Institute of Science）
地点(Place)：后主楼1124
时间(Time)：2026年9月22日（周二）16:00-17:00
邀请人(Inviter)：许孝精
报告摘要
We consider a three-dimensional rapidly rotating convection model of tall columnar structure. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. First, we analyze this system in the limit of infinite Prandtl number, i.e., when the momentum viscosity is much more dominant than the thermal diffusivity. Consequently, the dynamics of the velocity field take place at a much faster time scale than the temperature fluctuation, and at the limit the velocity field formally adjusts instantaneously to the thermal fluctuation. We prove the global well-posedness of weak solutions and strong solutions to this model. Second, we study the system in the absence of thermal diffusion. The lack of thermal diffusion introduces significant challenges in the analysis. To overcome these challenges, we first investigate the regularized model with thermal diffusion and establish delicate estimates that are independent of the thermal diffusion coefficient and consequently justify the vanishing diffusivity limit.
主讲人简介
Edriss S. Titi教授是国际知名应用数学家，现任英国剑桥大学非线性数学科学讲席教授，曾任美国得克萨斯农工大学杰出教授、Arthur Owen数学讲席教授及以色列魏茨曼科学研究所教授。他是美国数学学会首届会士、工业与应用数学学会会士及英国物理学会会士，并于2018年获古根海姆学者称号。他曾荣获德国洪堡研究奖，与合作者共同获得SIAM偏微分方程分析最佳论文奖及世界华人数学家联盟（ICCM）最佳论文金奖，并于2018—2020年担任德国柏林爱因斯坦访问学者。Titi教授长期致力于应用数学、非线性偏微分方程、流体动力学及无穷维耗散动力系统研究，重点研究Euler方程、Navier-Stokes方程及相关地球物理流体与湍流模型，研究方向涵盖大气与海洋动力学、数值分析、数据同化和控制理论。
