Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations

Abstract

We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity $\ddot{I}ƒ(T)$ for a given nonlinear dispersive equation, reducing the problem to the derivation of nonlinear smoothing estimates with a specific distribution of extra derivatives. We apply this strategy for both the defocusing generalized KdV and the nonlinear Schrödinger equations with odd pure-power nonlinearity. For both equations, we reach the lower bound $\ddot{I}ƒ(T)\gtrsim T^{-\frac{1}{2}-\hat{I}\mu }$, for any $\hat{I}\mu >0$, thus improving all available results in the current literature.

24 pages