Small scale formations in fluid equations with gravity
数学专题报告
报告题目(Title)：Small scale formations in fluid equations with gravity
报告人(Speaker)：姚珧 (新加坡国立大学)
地点(Place)： Zoom 会议 ID：880 143 16073, 密码：123456, Zoom Link: https://us02web.zoom.us/j/88014316073
时间(Time)： 2024 年 6 月 17 日（周一） 16:00--17:00
邀请人(Inviter)：薛留堂
报告摘要
In this talk, we discuss some PDEs that describe fluid motion under the influence of gravity, including the incompressible porous media equation and incompressible Boussinesq equation in two dimensions. Using an interplay between various monotone and conserved quantities, we construct rigorous examples of small scale formations as time goes to infinity. 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. (Based on joint works with Alexander Kiselev and Jaemin Park).
