Vol. 3, No. 2, 2021

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On the nonlinear regularized Schrödinger equation in exterior domains

Mohamed Karmous and Moez Khenissi

Vol. 3 (2021), No. 2, 361–393
Abstract

In this paper, we will establish, in two and three dimensions, the local well-posedness result in H01(Ω) of the nonlinear regularized Schrödinger equation using the Strichartz estimates for the regularized Schrödinger equation on exterior domains established previously. Then, we will prove, the global existence and uniqueness result in L2(Ω).

Keywords
nonlinear Schrödinger equation, exterior domain, exterior geometric control condition, Kato smoothing effect, Strichartz estimates
Mathematical Subject Classification 2010
Primary: 35B20, 35B65, 35Q41, 35Q55, 47H10
Milestones
Received: 3 October 2019
Revised: 22 April 2020
Accepted: 19 May 2020
Published: 5 December 2020
Authors
Mohamed Karmous
École Supérieure des Sciences et de Technologie de Hammam Sousse
Universite de Sousse
Tunisia
Moez Khenissi
École Supérieure des Sciences et de Technologie de Hammam Sousse
Universite de Sousse
Tunisia