吴家宏教授系列报告

发布时间:2018年06月04日 作者:唐颖   消息来源:业务办    阅读次数:[]

吴家宏教授系列报告 分3次安排,6月13日-6月15日 6月13日:10:30—12:00 6月14日:10:30—12:00 6月15日:10:30—12:00 Title: Global regularity and stability results for the?2D?Boussinesq equations with partial dissipation Abstract: This series of talks present recent work on the existence, uniqueness and stability problems concerning the 2D Boussinesq equations with partial dissipation. The Boussinesq equations model large scale atmospheric and oceanic flows that are responsible for cold fronts and the jet stream. In addition, the Boussinesq equations also play an important in the study of Rayleigh-Benard convection. Mathematically, The 2D Boussinesq equations retain some key features of the 3D Euler and Navier-Stokes equations such as the vortex stretching mechanism. It is hoped that the study of the Boussinesq equations will help us understand the Navier-Stokes millennium prize problem. We will cover the following materials. First, we describe the linear and nonlinear stability results on the hydrostatic equilibrium of the 2D Boussinesq equations with only velocity dissipation. This is a joint work with C. Doering, K. Zhao and X. Zheng. Second, we explain the existence and uniqueness of L^2 weak solutions to the general d-dimensional Boussinesq equations with only velocity dissipation. Third, we explain the work with L. Tao on the linear stability of the Couette flow for the 2D Boussinesq equations with only vertical dissipation. In addition, we will also report work in progress on the large-time behavior of perturbations of the hydrostatic equilibrium and on the nonlinear stability of the Couette flow. 专家简介:吴家宏教授现在是美国俄克拉荷马州立大学的校董会杰出教授和AT&T冠名教授. 他从北京大学获得计算数学学士学位和从芝加哥大学获得应用数学博士学位。芝加哥大学的数学系在北美排名前五. 吴家宏教授主要研究来自流体动力学、等离子物理、超导、地球物理、气象学等领域的非线性偏微分方程,目的是能够结合这些方程应用背景研究他们的一些基本数学理论。在曲面拟地转(surface quasi-geostrophic)方程、 Navier-Stokes方程、磁流体(magnetohydrodynamics)方程和 Boussinesq 方程解的整体存在性、唯一性和正则性等研究方面做出了突出贡献;已在Communications on Pure and Applied Mathematics、 Advances in Mathematics、 Archive for Rational Mechanics and Analysis等国际一流数学期刊上发表学术论文90余篇. 被同行引用超过4300次(据谷歌学者统计). 吴家宏教授与世界一流学术机构的顶尖科学家保持密切合作,包括 Peter Constantin等,取得了广泛的研究成果。吴家宏教授的这些研究成果受到了多项美国自然科学基金(NSF)的连续资助,同时候选人先后获得美国数学会“Centennial fellowship”奖、Oak Ridge 联邦大学(Associated Universities)Ralph E. Powe杰出青年奖、Oklahoma 州立大学“Celebrate State”奖以及Oklahoma州 Regents杰出研究奖等,这些都充分显示了吴家宏教授的研究已在国际上被高度肯定。



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