Multisoliton solutions and blow up for the $L^2$-critical Hartree equation
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| Format: | Preprint |
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2025
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| _version_ | 1866915129449250816 |
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| author | Gómez, Jaime Schmid, Tobias Wu, Yutong |
| author_facet | Gómez, Jaime Schmid, Tobias Wu, Yutong |
| contents | We construct multisoliton solutions for the $L^2$-critical Hartree equation with trajectories asymptotically obeying a many-body law for an inverse square potential. Precisely, we consider the $m$-body hyperbolic and parabolic non-trapped dynamics. The pseudo-conformal symmetry then implies finite-time collision blow up in the latter case and a solution blowing up at $m$ distinct points in the former case. The approach we take is based on the ideas of [Krieger-Martel-Raphaël, 2009] and the third author's recent extension. The approximation scheme requires new aspects in order to deal with a certain degeneracy for generalized root space elements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multisoliton solutions and blow up for the $L^2$-critical Hartree equation Gómez, Jaime Schmid, Tobias Wu, Yutong Analysis of PDEs Primary: 35B40. Secondary: 35B44 We construct multisoliton solutions for the $L^2$-critical Hartree equation with trajectories asymptotically obeying a many-body law for an inverse square potential. Precisely, we consider the $m$-body hyperbolic and parabolic non-trapped dynamics. The pseudo-conformal symmetry then implies finite-time collision blow up in the latter case and a solution blowing up at $m$ distinct points in the former case. The approach we take is based on the ideas of [Krieger-Martel-Raphaël, 2009] and the third author's recent extension. The approximation scheme requires new aspects in order to deal with a certain degeneracy for generalized root space elements. |
| title | Multisoliton solutions and blow up for the $L^2$-critical Hartree equation |
| topic | Analysis of PDEs Primary: 35B40. Secondary: 35B44 |
| url | https://arxiv.org/abs/2501.18398 |