Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions and its applications
数学专题报告
报告题目(Title)：Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions and its applications
报告人(Speaker)：Jeaheang Bang (UT San Antonio)
地点(Place)：ZoomID: 952 0206 9493 密码: 305143
时间(Time)：2023 年 11月 10日09：30—10：30
邀请人(Inviter)：熊金钢
报告摘要
Solutions with scaling-invariant bounds, such as self-similar solutions, play an important role in the understanding of the regularity and asymptotic structures of solutions to the Navier-Stokes equations. We recently proved that any steady solution satisfying |u(x)|≤C|x| for any constant C in R^n∖{0} with n≥4, must be zero without imposing a smallness or self-similarity assumption. Our main idea is to analyze the velocity field and the total head pressure via weighted energy estimates with suitable multipliers, and our proof is pretty elementary and short. These results not only give the Liouville-type theorem for steady solutions in higher dimensions but also help to remove a class of singularities of solutions and give the optimal asymptotic behaviors of solutions at infinity in the exterior domains. This is a joint work with Changfeng Gui, Hao Liu, Yun Wang and Chunjing Xie.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
