An Optimal Decay Estimate for the Linearized Water Wave Equation in 2D

Thursday, May 28, 2015 - 3:00pm - 3:30pm
Lind 305
Aynur Bulut (University of Michigan)
In this talk, we discuss recent work concerning a decay estimate for solutions to the linear dispersive equation iu_t-(-Delta)^{1/4}u=0, for (t,x)in R times R, which corresponds to a factorization of the linearized two-dimensional water wave equation. Our arguments are based on a Littlewood-Paley decomposition and stationary phase estimates, and we obtain optimal decay of order t^{-1/2} for solutions, assuming only bounds in L^2-based spaces (with weights).