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

Luigi Forcella; Vladimir Georgiev

arxiv: 2410.16039 · v1 · pith:35JCNJPHnew · submitted 2024-10-21 · 🧮 math.AP · math-ph· math.MP

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

Luigi Forcella , Vladimir Georgiev This is my paper

classification 🧮 math.AP math-phmath.MP

keywords blow-upenergyestablishinteractionlocalpointspacewell-posedness

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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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