会议时间：2024/06/19  09:30 -10:30

会议地点：数学统计楼213

报告人： 罗巍 副教授 （中山大学）

报告题目：The Liouville theorem for the stationary Navier-Stokes equations

报告摘要：

The Liouville type theorem is an old open problem(See Leray JMPA, 1933). In this talk, we will recall the results and history. Under the general integrability condition, we prove the pointwise decay estimate of the vorticity $\omega$ and obtain the Liouville-type theorem. This is baed on the joint work with Yupei Li

个人简介：罗巍，中山大学数学学院副教授，主要研究复杂流体与浅水波相关的偏微分方程，在ARMA, Adv. Math，JDE等期刊上发表论文20余篇，主持国自然青基和广东省面上项目各一项。

    会议时间：2024/06/19  10:30-11:30

会议地点：数学统计楼213

报告人：  郭颖颖 （佛山大学）

报告题目：The well-posedness and ill-posedness for the Hunter-Saxton equation on the line

报告摘要：

In this talk, I will give an exact division for the well-posedness and ill-posedness (non-existence) of the Hunter-Saxton equation on the line. More precisely, if u_0∈B∩H ̇^1 (R), we establish the local well-posedness of the Cauchy problem for the Hunter-Saxton equation. Contrariwise, if u_0∈B but u_0∉H ̇^1 (R), the norm inflation occurs and hence the ill-posedness is presented. Our result clarifies a corollary with physical significance such that all the smooth solutions in L^∞ (0,T;L^∞ (R) ) must have the H ̇^1 norm.This is based on the joint work with Weikui Ye and Zhaoyang Yin.