On no-return theorems in nonlinear dispersive PDEs
Speaker: Wilhelm SCHLAG, Yale
Location: Warren Weaver Hall 1302
Date: Thursday, November 14, 2019, 11 a.m.
In 2010 Nakanishi and the speaker introduced a "one-pass
theorem" which precludes solutions to nonlinear wave equations
starting from a small neighborhood of a ground state soliton and which
return to another such neighborhood after some finite time. Such
statements are non-perturbative and require global arguments. In the
original setting invariant manifolds played an essential role,
especially the one-dimensional unstable manifold associated with the
steady-state solution. I will review these results, and discuss some
of their ramifications over the past ten years.