报告题目：Long time behavior of two dimensional fluid flows at high Reynolds numbers

报 告 人：Hao Jia

报告人所在单位：University of Minnesota

报告日期：2025年6月9日

报告时间：10:00

报告地点：光华楼东主楼 2201

报告摘要：The two dimensional incompressible Navier Stokes equations with small viscosity (corresponding to large Reynolds numbers) play a fundamental role in modeling large scale behavior of fluid flows, such as atmospheric turbulence, Due to the small (or zero) viscosity and lack of global relaxation mechanism for the limiting Euler equation, the long time behavior of solutions is challenging to study mathematically, even in perturbative regimes. The main difficulties are the presence of continuous spectrum, non-self-adjointness of associated linear operators, singular perturbations and strong nonlinear effects.

In this talk, we will review some recent progress on understanding precise dynamics near coherent solutions, such as shear flows and vortices, including linear and nonlinear inviscid damping results enhanced dissipation effects and vorticity depletion phenomena. Numerical simulations, major open problems and future directions will also be presented.

个人简介：Hao Jia is an associate professor at the University of Minnesota. Jia obtained his PhD at the University of Minnesota in 2013 under the supervision of Vladimir Sverak, and was a Dickson instructor at the University of Chicago from 2013 to 2016 where he was mentored by Carlos Kenig and Wilhelm Schlag. He spent one year as a member at the institute for Advanced Study from 2016 to 2017, before joining the University of Minnesota as an assistant professor (associate professor from 2022). Hao Jia's main research interests are Partial Differential Equations motivated by mathematical physics. He has publications in Inventiones, Acta Math., GAFA, CPAM, CMP, ARMA among others.

海报：Hao Jia 学术报告.jpg