题目：Benjamin-Ono soliton dynamics in a slowly varying potential 

报告人：张芷媛 (Courant Institute, NYU) 

时间：6月7日周一上午9:00-10:00

地点：Zoom会议ID：7361907370 密码:122595

摘要：We consider the Benjamin-Ono equation, modeling one-dimensional long interval waves in a stratified fluid, with a slowly-varying potential perturbation. Starting with near soliton initial data, we prove that the solution remains close to a soliton wave form, with parameters of position and scale evolving according to effective ODEs depending on the potential. The result is valid on a time-scale that is dynamically relevant, and highlights the effect of the perturbation. In particular, we are able to prove an “exact” parameter dynamics for the soliton. This is achieved by a Lyapunov functional built from energy and mass, Taylor expansions, spectral estimates, and estimates for the Hilbert transform, with a local virial estimate for the linearized equation.