Control of the Schr\"{o}dinger equation in $\mathbb{R}^3$: The critical case
Abstract
This article deals with the $\dot{H}^{1}$--level exact 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 exact controllability for the critical nonlinear Schr\"{o}dinger equation.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2024
- arXiv:
- arXiv:2404.07749
- Bibcode:
- 2024arXiv240407749S
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Optimization and Control
- E-Print:
- 20 pages. Comments are welcome