Colette Guillope : Global existence of solutions for a fractional damped Schrödinger equation

Posted by Jerry Bona , part of the Analysis and Applied Mathematics Seminar.

At

Oct. 10, 2022, 4 p.m.

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1227 SEO

Abstract

We consider the initial value problem for the fractional nonlinear Schrödinger equation with a damping term. We study the global existence and the scattering of solutions. Noticeably, for the focusing nonlinearity, it is shown that for a large enough damping, the size of the solution depends only on the initial data, and the solution exists for all times in a space of regular enough functions.