Space time resonances and scattering of the Zakharov system.

Thursday, September 27, 2012 - 9:00am - 9:50am
Keller 3-180
Jalal Shatah (New York University)
We will present a new extension of the space time resonance method to show global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in $3$ space dimensions. The wave component is shown to decay pointwise at the optimal rate of $t^{-1}$,
whereas the S component decays almost at a rate of $t^{-7/6}$. This is a joint work with Z. Hani and F. Pusateri.