Gain of analyticity for semilinear Schroedinger equations

Details Gain of analyticity for semilinear Schroedinger equations Gain of analyticity for semilinear Schroedinger equations

2007-08-16

arxiv.org/abs/0708.2154v3

Mathematics

Analysis of PDEs

37 pages, no figure, minor change

Scientific paper

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.

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