Control of the Schrödinger equation in $\mathbb{R}^3$: The critical case
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos |
| author_facet | Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos |
| contents | This article deals with the $H^{1}$--level local null controllability for the energy-critical nonlinear Schrödinger 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 Schrödinger equation to be controllable. Finally, we use a perturbation argument and show local controllability for the critical nonlinear Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Control of the Schrödinger equation in $\mathbb{R}^3$: The critical case Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos Analysis of PDEs Optimization and Control This article deals with the $H^{1}$--level local null controllability for the energy-critical nonlinear Schrödinger 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 Schrödinger equation to be controllable. Finally, we use a perturbation argument and show local controllability for the critical nonlinear Schrödinger equation. |
| title | Control of the Schrödinger equation in $\mathbb{R}^3$: The critical case |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2404.07749 |