# American Institute of Mathematical Sciences

September  2020, 9(3): 721-732. doi: 10.3934/eect.2020030

## Remarks on the damped nonlinear Schrödinger equation

 Departement of Mathematics, College of Sciences and Arts of Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia

Received  June 2019 Revised  August 2019 Published  December 2019

It is the purpose of this note to investigate the initial value problem for a focusing semi-linear damped Schrödinger equation. Indeed, in the energy sub-critical regime, one obtains global well-posedness and scattering in the energy space, depending on the order of the fractional dissipation.

Citation: Tarek Saanouni. Remarks on the damped nonlinear Schrödinger equation. Evolution Equations & Control Theory, 2020, 9 (3) : 721-732. doi: 10.3934/eect.2020030
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