报告题目：Small scale formation for the 2D Boussinesq equation
报告人：姚珧 教授 National University of Singapore, Singapore
报告摘要：In this talk, we consider the 2D incompressible Boussinesq equation without thermal diffusion, and aim to construct rigorous examples of small scale formations as time goes to infinity. In the viscous case, we construct examples of global-in-time smooth solutions where the H^1 norm of density grows to infinity algebraically in time. For the inviscid equation in the strip, we construct examples whose vorticity grows at least like t^3 and gradient of density grows at least like t^2 during the existence of a smooth solution. These growth results work for a broad class of initial data, where we only require certain symmetry and sign conditions. As an application, we also construct solutions to the 3D axisymmetric Euler equation whose velocity has infinite-in-time growth. This is a joint work with Alexander Kiselev and Jaemin Park.
报告人简介：Yao Yao is currently a Dean’s Chair Associate Professor of Mathematics at the National University of Singapore. She received her BS degree from Peking University in 2007, and PhD degree in 2012 from UCLA. She was a Van Vleck Visiting Assistant Professor at University of Wisconsin-Madison in 2012-2015, and an Assistant Professor at Georgia Institute of Technology in 2015-2021. Her research focuses on the analysis of partial differential equations arising in mathematical biology and fluid dynamics, especially on the equations with a nonlocal transport term. She was a recipient of the NSF CAREER Award in 2018 and Sloan Research Fellowship in 2020.