Remarks on the damped nonlinear Schrödinger equation

Tarek Saanouni

doi:10.3934/eect.2020030

Article Contents

2020, Volume 9, Issue 3: 721-732. Doi: 10.3934/eect.2020030

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Remarks on the damped nonlinear Schrödinger equation

Tarek Saanouni

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

Received: June 2019

Revised: August 2019

Early access: December 13, 2019

Published online: December 13, 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 37K10.

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References

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