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arXiv · 2601.05341

Threshold solutions for the $3d$ cubic INLS: the energy-subcritical case

Luccas Campos·Luiz Gustavo Farah·Jason Murphy
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Abstract

We revisit the work [L. Campos and J. Murphy, SIAM J. Math. Anal., 55 (2023), pp. 3807--3843], which classified the dynamics of $H^1$ solutions at the ground state threshold for cubic inhomogeneous nonlinear Schr\"odinger equations of the form $i\partial_t u + \Delta u + |x|^{-b}|u|^2 u = 0$ in the range $b\in(0,\tfrac12)$. By modifying the modulation analysis and using Strichartz estimates in place of pointwise bounds, we extend the result to the full energy-subcritical range $b\in(0,1)$. This strategy is expected to carry over to other dispersive equations with singular potentials.

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Luccas Campos, Luiz Gustavo Farah, Jason Murphy. 2026-01-08. Threshold solutions for the $3d$ cubic INLS: the energy-subcritical case. https://arxiv.org/abs/2601.05341

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