Multisoliton Solutions and Blow Up for the $$L^2$$-Critical Hartree Equation
Abstract
Abstract We construct multisoliton solutions for the $$L^2$$ L 2 -critical Hartree equation with trajectories asymptotically obeying a many-body law for an inverse square potential. More 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 [10] and the third author’s recent extension [36]. The approximation scheme requires new aspects in order to deal with a certain degeneracy for generalized root space elements.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Waves and Solitons
Black Holes and Theoretical Physics
Publication details
- Journal / source
- Archive for Rational Mechanics and Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 250
- Issue
- 5
- Publication date
- 22 August 2026
- Language
- EN