报告题目：Emergent Singular Solutions (ESS) of Nonlinear Wave Equations
报告人：Darryl Holm(英国帝国理工学院 教授)
报告时间：2023年02月22日下午5:00开始
报告地点：Zoom meeting: 9138029559，Password: 895852
报告摘要：We discuss emergent singular solutions (ESS) in nonlinear wave PDEs.
(1) Start with asymptotic expansion for 1D shallow water waves.
(2) Identify the b-equation in n dimensions, H-Staley [2003]
In 1D, b = 2 Camassa-H [1993], b = 3 Degasperis-Processi [2002]
(3) Q: Why is b = 2 special? Is ESS is a property of integrability?
A: No. The ESS Ansatz is a momentum map, H-Marsden [2005]
(4) Are there other geodesic ESS with b = 2 in 1D? Fringer-H [2001]
(5) ESS for Stochastic CH? Crisan-H [2019] & Bendall-Cotter-H [2022]
(6) Are there ESS for b = 2 and W 1,r norm? Cotter-H-Pryer [2023]
(7) Are there ESS embeddings for PDEs in 2D & 3D?. H-Staley [2004].
报告人简介：Darryl D Holm is a Professor of Mathematics at Imperial College London.Before coming to Imperial College London in 2005 as Professor of Mathematics, Holm spent thirty four years at Los Alamos National Laboratory.His work involves formulating and analysing model continuum partial differential equations. These continuum models have been applied, for example, to investigate nonlinear waves such as solitons, turbulence, geophysical fluid dynamics (GFD) in climate change and weather variability etc. He introduced the well-known Camassa-Holm equation from sallow water wave propagation.Holm has developed a wide range of interests, many of which were informed by his geometric approach to dynamical systems.
He has been the associate editors or editors of Physics Letters A, SIAM J. Appl. Dynamical Systems, Dynamics of PDE, Journal of Physics A: Mathematical and Theoretical, Journal of Geometric Mechanics, Journal of Nonlinear Science, SIGMA etc.He is PI of many grants includingRoyal Society Wolfson Research Merit Award , United States Office of Naval Research Grant, Non-Linear Internal Wave Initiative (NLIWI)，European Research Council Advanced Grant，UK EPSRC Standard Grant etc.
