Gain of analyticity for semilinear Schrödinger equations. (English) Zbl 1155.35091
Summary: We discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear Schrödinger 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35B45 | A priori estimates in context of PDEs |
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