The Modified Energy Method for a Nonlocal Quasilinear Wave Equation

Ryan Martinez (UC, Berkeley)

Jun 18. 2024, 15:15 — 15:30

In this talk I will focus on how the Modified Energy Method of Hunter-Ifrim-Tataru-Wong can be applied in situations where it is unclear what normal form transformation to use. We will use a nonlocal, quasilinear wave equation of Kirchhoff type, which I and Tataru have been working on to illustrate the method. In this problem the gain is an enhanced cubic lifespan for small initial data in $H^{5/4} \times H^{1/4}$. Previously smallness was only guaranteed on a quadratic time scale and depended on the initial data in $H^{3/2} \times H^{1/2}$.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Nonlinear Waves and Relativity (Thematic Programme)
Organizer(s):
Roland Donninger (U of Vienna)
David Fajman (U of Vienna)
Birgit Schörkhuber (U of Innsbruck)