Title: Spacetime resonance and asymptotic behavior for wave equations

Date: 11/29/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Yu Deng, Courant Institute of Mathematical Sciences, NYU

The method of spacetime resonance was developed by Germain-Masmoudi-Shatah to study small data long time problems for nonlinear dispersive equations. In this talk we will consider the wave equation □u=uΔu in 3+1 dimensions. Global existence for this equation was proved by Lindblad and Alinhac. By applying the method of spacetime resonance, we are able to obtain the precise asymptotics for small solutions, which turns out to exhibit a subtle nonlinear behavior. Our work also justifies the ideas behind a conjecture of Lindblad and Rodnianski. This is joint work with F. Pusateri.