题目：Stability of Solitary Waves to the Shallow Water Models
时间：2021.9.25 (周六)，9:00--10:00
地点：腾讯会议（会议ID：780 7596 4755）
报告人：刘跃(Yue Liu)教授,德克萨斯大学阿林顿分校
https://meeting.tencent.com/s/GUY2wyMDbqag
摘要：
In this talk, we will present our recent results on dynamical stability of localized smooth solitary waves to the Desgasperis-Procesi (DP) equation and modified Camassa-Holm (mCH) equation on the real line. Those quasilinear equations are completely integrable and arise as asymptotic models for the unidirectional propagation of shallow water waves. The crucial ingredient in our approach to the DP case is to observe that the $L^\infty$ orbital norm of the perturbation is bounded above by a function of its $L^2$ orbital norm, yielding the orbital stability in the L^2\cap L^\infty$ space. We also show orbital stability of the smooth solitary-wave solution of the mCH equation in the energy space $ H^1 \cap W^{1, 4} $ under small disturbances by variational methods without the assumption on the positive momentum density initially.
报告人简介：
刘跃，美国德克萨斯大学阿灵顿分校教授，1994年获布朗大学博士学位，师从国际著名数学家Walter Strauss教授。在偏微分方程，应用分析和流体力学，可积系统与孤子理论，非线性波方程的稳定性理论、奇异性形成、局部和整体适定性等领域取得国际领先的成果。在“Comm. Pure Appl. Math.”、“Adv. Math.”、“Comm. Math. Phys.”、“Arch. Ration.Mech. Anal.”、“J. Funct. Anal.”、“Physica D”、“J. Differential Equations”、“Nonlinearity”、“Quart. of Appl. Math.”等国际著名刊物上发表论文90余篇。
欢迎广大师生参加！
