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arXiv · 2001.11613

Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation

Luccas Campos·Mykael Cardoso
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Abstract

We consider the inhomogeneous nonlinear Schr\"odinger equation (INLS) in $\mathbb{R}^N$, $N \geq 1$, $$i \partial_t u + \Delta u + |x|^{-b} |u|^{p-1}u = 0,$$ with finite-variance initial data $u_0 \in H^1(\mathbb{R}^N)$. We extend the dichotomy between scattering and blow-up for solutions above the mass-energy threshold (and with arbitrarily large energy). We also show other two blow-up criteria, wich are valid in any mass-supercritical setting, given there is local well-posedness.

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Luccas Campos, Mykael Cardoso. 2020-01-31. Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation. https://arxiv.org/abs/2001.11613

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