Control of the Schrödinger equation in \(\mathbb{R}^3\): The critical case

This article deals with the \(H^{1}\)--level local null controllability for the defocusing critical nonlinear Schr\"{o}dinger equation in \(\mathbb{R}^3\). Firstly, we show the problem under consideration to be well-posed using Strichartz estimates. Moreover, through the Hilbert uniqueness meth...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Silva, Pablo Braz e, Roberto de A Capistrano-Filho, Jackellyny Dassy do Nascimento Carvalho, dos Santos Ferreira, David
Format: Article
Language:English
Subjects:
Controllability
Defocusing
Schrodinger equation
Online Access:Get full text
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Summary:This article deals with the \(H^{1}\)--level local null controllability for the defocusing critical nonlinear Schr\"{o}dinger equation in \(\mathbb{R}^3\). Firstly, we show the problem under consideration to be well-posed using Strichartz estimates. Moreover, through the Hilbert uniqueness method, we prove the linear Schr\"{o}dinger equation to be controllable. Finally, we use a perturbation argument and show local controllability for the critical nonlinear Schr\"{o}dinger equation.
ISSN:2331-8422