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arXiv · 2601.05349

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

Luccas Campos·Luiz Gustavo Farah·Jason Murphy
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Abstract

We study the energy-critical $3d$ cubic inhomogeneous NLS equation $i\partial_t u + \Delta u + |x|^{-1}|u|^2 u=0$. In this work, we prove the existence of special solutions $W^\pm$ with energy equal to that of the ground state $W$ and use these solutions to characterize the behavior of solutions at the ground state energy. The singular factor $|x|^{-1}$ in the nonlinearity significantly limits the smoothness of the ground state and prompts a novel approach to the modulation analysis.

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Luccas Campos, Luiz Gustavo Farah, Jason Murphy. 2026-01-08. Threshold solutions for the $3d$ cubic INLS: the energy-critical case. https://arxiv.org/abs/2601.05349

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