Multisoliton solutions and blow up for the $L^2$-critical Hartree equation
Analysis of PDEs
2025-01-31 v1
Abstract
We construct multisoliton solutions for the -critical Hartree equation with trajectories asymptotically obeying a many-body law for an inverse square potential. Precisely, we consider the -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 distinct points in the former case. The approach we take is based on the ideas of [Krieger-Martel-Rapha\"el, 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.
Keywords
Cite
@article{arxiv.2501.18398,
title = {Multisoliton solutions and blow up for the $L^2$-critical Hartree equation},
author = {Jaime Gómez and Tobias Schmid and Yutong Wu},
journal= {arXiv preprint arXiv:2501.18398},
year = {2025}
}