报告题目：Ill-posedness of the Novikov equation in the critical Besov space $B^1_{\infty,1}(R)$

报告时间：2023年2月24日上午10：00-11：00

报告地点：腾讯会议，会议号：457-229-222

主持人：关春霞

摘要 ：It is shown that both the Camassa-Holm and Novikov equations are ill-posed in $B_{p,r}^{1+1/p}(\mathbb{R})$ with $(p,r)\in[1,\infty]\times(1,\infty]$ in \cite{Guo2019} and well-posed in $B_{p,1}^{1+1/p}(\mathbb{R})$ with $p\in[1,\infty)$ in \cite{Ye}. Recently, the ill-posedness for the Camassa-Holm equation in $B^{1}_{\infty,1}(\R)$ has been proved in \cite{Guo}.

In this paper, we shall solve the only left an endpoint case $r=1$ for the Novikov equation. More precisely, we prove the ill-posedness for the Novikov equation in $B^{1}_{\infty,1}(\R)$ by exhibiting the norm inflation phenomena.

报告人简介：李金禄现为赣南师范大学副教授，主要研究方向为偏微分方程的数学理论。相关成果已发表于Advances in Mathematics, Journal of Functional Analysis, Journal of Differential Equations, Journal of Nonlinear Science, Journal of Geometric Analysis等国际期刊。