报告人：闫威（河南师范大学）

邀请人：杨美华

报告时间：2020年12月10日（星期四）上午9: 00 -11：00

报告地点：腾讯会议ID：141 498 885

报告题目：Probabilistic Cauchy problem for the generalized KdV equation

报告摘要：In this talk, by using the Fourier restriction norm method, we consider the Cauchy problem for a generalized KdV equation u_{t}+\partial_{x}^{3}u+\frac{1}{k+1}(u^{k+1})_{x}=0,k\geq5 with random data.By using the Wiener randomization of the initial data, Strichartz estimates and probabilistic Strichartz estimates, we establish the probabilistic well-posedness in $H^{s_{1}}(\R)\left(s>{\rm max}\left\{\frac{1}{k+1}\left(\frac{1}{2}-\frac{2}{k}\right),\frac{1}{6}-\frac{2}{k}\right\}\right)$ with random data.We also prove that the stochastic continuity of free KdV equation holds with random data belonging to $L^{2}([0,2\pi))$ almost surely. Our result improves the result of Hwang, Kwak (Proc. Amer. Math. Soc. 146(2018), 267-280.). Our method can be applied to probabilistic well-posedness problem of other KdV-type equations with random data in supercritical case.

报告人简介： 闫威, 河南师范大学教授. 研究兴趣包含无穷维动力系统与随机无穷维动力系统以及发展方程的初值随机化，取得了系列深刻的结果。先后在JDE, NA等国际学术期刊上发表学术论文20余篇。主持天元基金、青年基金、面上基金各一项。