BYR Achieve · 镜像论坛

理学院“青年学术论坛”第42期

2015/3/18镜像同步0 回复

理学院“青年学术论坛”第42期讲座题目：Well-posedness of Camassa-Holm equation in the endpoint space $H^{3/2}$ 主讲人：霍朝辉副研究员(中科院数学与系统科学研究院)主持人：陈秀卿教授时间：2015年3月20日（周五）上午10:00-11:00地点：主楼1214 主要内容：We mianly consider the well-posedness of the Cauchy problem for Camassa-Holm equation. The local well-posedness for Camassa-Holm equation was obtained applying Kato's semigroup approach [G.R.Blanco,2001] in $H^{s}$ with $s>3/2$. Moteover, by using the transport equation theory and the Besov spaces,Danchin [R.Danchin,2003] proved that the Cauchy problem for the Camassa-Holm equation is locally well-posed in $B^{3/2}_{2,1}$. Counterexamples to well-posedness in thecase $s<3/2 $ have been exhibited by Himonas and Misiolek [A. Himonas, G. Misiolek,2001] actually what they do prove there is that uniform continuity with respect to the data cannot hold in $H^s$ with $s<3/2 $). Therefore, in the Sobolev spaces framework, $s=3/2$ seems to be thecritical value for local well-posedness. We can show that if $u_0 \in H^{3/2}(\R)$ and $u_0-u_{0xx} $ does not change signand belongs to $L^1$; then the Cauchy problem of Camassa-Holm equation is locally well-posed in endpoint space $H^{3/2}$. The flow map $u_0\rightarrow u(t)$ is also continuous. 主讲人霍朝辉简介: 2007/03 – 至今，中科院, 数学与系统科学研究院数学所, 副研究员. 2007/02 – 2009/02, 香港城市大学, 数学系, Research Fellow。 2006/06 – 2007/03, 中科院, 数学与系统科学研究院数学所, 助理研究员. 2004/06 – 2006/06, 北京航空航天大学, 数学系, 博士后, 2001/09 – 2004/06，中国工程物理研究院北京研究生部 (主页http://sourcedb.amss.cas.cn/zw/zjrck/fyjy/200910/t20091016_2552552.html) 理学院2015年3月18日 http://portal.bupt.edu.cn//html/main/col38/2015-03/18/20150318090047566207481_1.html

订阅后，新回复会通过你的通知中心匿名送达。