Gain of analyticity for semilinear Schroedinger equations
Analysis of PDEs
2008-06-15 v3
Abstract
We discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear Schroedinger equations with gauge invariant nonlinearity. We prove that if the initial data decays exponentially, then the solution becomes real-analytic in the space variable and a Gevrey function of order 2 in the time variable except in the initial plane. Our proof is based on the energy estimates developed in our previous work and on fine summation formulae concerned with a matrix norm.
Cite
@article{arxiv.0708.2154,
title = {Gain of analyticity for semilinear Schroedinger equations},
author = {Hiroyuki Chihara},
journal= {arXiv preprint arXiv:0708.2154},
year = {2008}
}
Comments
37 pages, no figure, minor change