長沙理工大學學術活動預告
報告承辦單位: 數學與統計學院
報告內容: Thermal Stratification in Geophysical Fluid Flows
報告人姓名: 趙昆
報告人所在單位: 杜蘭大學
報告人職稱/職務及學術頭銜:副教授
報告時間: 2020年1月6日（周一）下午16：00-17:00
報告地點: 云理科樓A419
報告人簡介:趙昆，男，40歲，博士生導師，主要研究領域為流體動力學中的偏微分方程、生物數學中的偏微分方程，1997-2004年中國科學技術大學本碩連讀，2004-2009年美國佐治亞理工學院博士研究生畢業，2009-2011年美國生物數學研究所博士后出站，2011-2012年美國愛荷華大學訪學一年, 2012年進入美國杜蘭大學工作，2018年晉升為杜蘭大學副教授。自博士畢業以來，在國際數學頂尖級期刊上如《Journal of Differential Equations》,《Indiana University Mathematics Journal》,《Archive for Rational Mechanics and Analysis》,《SIAM Journal on Mathematical Analysis》公開發表或已投稿論文55篇，已發表論文被SCI收錄45篇，主持西蒙斯基金會資助數學家項目1項，，獲得LA BoR Research Competitiveness Subprogram 項目1項，獲得MBI Early Career資助項目1項，獲得杜蘭大學 CoR Research Fellowship項目1項，長期擔任《Journal of European Mathematical Society》,《Journal of Differential Equations》,《SIAM Journal on Mathematical Analysis》,《Nonlinearity》等30多種SCI雜志審稿專家，2015年被評為《Journal of Differential Equations》,《Journal of Mathematical Analysis and Applications》等雜志有突出貢獻的審稿專家，現已培養博士后3人出站，8人博士畢業，30人碩士畢業，現為美國數學學會，美國工業與應用數學學會,美國MAA委員。
報告摘要：he two-dimensional incompressible Boussinesq equations
have been routinely used to model systems across a
tremendous range of length and time scales from
microfluidics and biophysics to geodynamics and astrophysics. It plays an important role in the study of atmospheric and oceanographic turbulence as well as other situations where rotation and stratification play a dominant role. In addition to its own physical background, the model is also known for its close connection with fundamental models in mathematical fluid mechanics, such as the incompressible Euler and Navier-Stokes equations. In a special situation, the vortex formulation of this two-dimensional model in Eulerian coordinates is formally identical to the vortex formulation of the three-dimensional Euler equations in cylindrical coordinates for axisymmetric swirling fluid flows, which makes it a tremendously rich area for mathematical investigations. The theme of this talk is oriented around the rigorous mathematical demonstration of one of the common phenomena in geophysical fluid flows: thermal (vertical) stratification. In addition, some recent results on the stability of dynamic shear flow will be reported. Moreover, some open problems and numerical experiments will be discussed.