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arXiv · 2106.09139

Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold

Alex H. Ardila
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Abstract

In this paper, we study the nonlinear Schr\"odinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on Kenig-Merle's compactness-rigidity argument. Then we prove the energy scattering below and above the mass-energy threshold. We also describe the dynamics of solutions with data at the ground state threshold. Finally, we prove a blow-up criteria for the equation with initial data with arbitrarily large energy.

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Alex H. Ardila. 2021-06-16. Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold. https://doi.org/10.1016/j.physd.2021.132978

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