turkmath.org

In this talk we consider the initial value problem for the Fornberg-Whitham equation, a one dimensional shallow water model allowing wave breaking. We write the equations as a second order ODE on an infinite dimensional manifold. Using this formulation we show that for T>0 the time T solution map of the Fornberg-Whitham equation, i.e. the operator mapping the initial data u(t=0) to the time T value u(t=T) of the solution, is nowhere locally Lipschitz and nowhere C^1. 

Link to the seminar:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1607157398833?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d