Threshold solutions for the $3d$ cubic INLS: the energy-subcritical case
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| Format: | Preprint |
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2026
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| author | Campos, Luccas Farah, Luiz Gustavo Murphy, Jason |
| author_facet | Campos, Luccas Farah, Luiz Gustavo Murphy, Jason |
| contents | 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 Schrödinger equations of the form $i\partial_t u + Δu + |x|^{-b}|u|^2 u = 0$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Threshold solutions for the $3d$ cubic INLS: the energy-subcritical case Campos, Luccas Farah, Luiz Gustavo Murphy, Jason Analysis of PDEs 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 Schrödinger equations of the form $i\partial_t u + Δu + |x|^{-b}|u|^2 u = 0$ 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. |
| title | Threshold solutions for the $3d$ cubic INLS: the energy-subcritical case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.05341 |