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arXiv · 2410.16039

Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction

Luigi Forcella·Vladimir Georgiev
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Abstract

We consider the two-dimensional nonlinear Schr\"odinger equation with point interaction and we establish a local well-posedness theory, including blow-up alternative and continuous dependence on the initial data in the energy space. We provide a proof by employing a Kato's method along with Hardy inequalities with logarithmic correction. Moreover, we establish finite time blow-up for solutions with positive energy and infinite variance.

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Luigi Forcella, Vladimir Georgiev. 2024-10-21. Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction. https://doi.org/10.1017/prm.2025.10037

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