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arXiv · 2404.07749

Control of the Schr\"{o}dinger equation in $\mathbb{R}^3$: The critical case

Pablo Braz e Silva·Roberto de A. Capistrano-Filho·Jackellyny Dassy do Nascimento Carvalho·David dos Santos Ferreira
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Abstract

This article deals with the $H^{1}$--level local null controllability for the energy-critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$. Firstly, we demonstrate that the problem under consideration is 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.

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Pablo Braz e Silva, Roberto de A. Capistrano-Filho, Jackellyny Dassy do Nascimento Carvalho, David dos Santos Ferreira. 2024-04-11. Control of the Schr\"{o}dinger equation in $\mathbb{R}^3$: The critical case. https://arxiv.org/abs/2404.07749

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