Asymmetric minimal mass blow-up for the quintic NLS on a star graph
Abstract
This work is concerned with the focusing quintic nonlinear Schrödinger equation on a star graph with two edges, with a delta interaction of arbitrary strength at the vertex. We construct a non-radial, minimal mass, finite time blow-up solution, whose singularity forms at an arbitrarily prescribed interior point of one edge. Our approach is based on a suitable cut-off of the standard pseudoconformal blow-up solution of the focusing quintic NLS on the line, inspired by Ogawa-Tsutsumi and Burq-Gérard-Tzvetkov. A noteworthy feature of our construction is the persistence of the domain of the Hamiltonian under the flow, obtained by the persistence of regularity method of Kato. We also identify a two-parameter family of distinct blow-up profiles, which should play a central role in the classification of non-radial minimal mass blow-up solutions on the star graph. Our construction is generic and can be extended to a star graph with an arbitrary number of edges. It can certainly also be adapted to other types of metric graphs.
Related
- Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
- Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS
- An Exact Mass Threshold for Global Existence and Blow-up in Semilinear Anti-de Sitter Equations
- Explicit strong blocking sets and minimal codes from expander graphs using a new graph parameter
- Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the L2-critical level
BibTeX
@misc{buratti2026asymmetric,
title = {{Asymmetric minimal mass blow-up for the quintic NLS on a star graph}},
author = {Mattia Buratti and François Genoud and Vladimir Georgiev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13752},
eprint = {2610.13752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13752},
}
RIS
TY - UNPB
TI - Asymmetric minimal mass blow-up for the quintic NLS on a star graph
AU - Mattia Buratti
AU - François Genoud
AU - Vladimir Georgiev
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13752
UR - https://arxiv.org/abs/2610.13752
AB - This work is concerned with the focusing quintic nonlinear Schrödinger equation on a star graph with two edges, with a delta interaction of arbitrary strength at the vertex. We construct a non-radial, minimal mass, finite time blow-up solution, whose singularity forms at an arbitrarily prescribed interior point of one edge. Our approach is based on a suitable cut-off of the standard pseudoconformal blow-up solution of the focusing quintic NLS on the line, inspired by Ogawa-Tsutsumi and Burq-Gérard-Tzvetkov. A noteworthy feature of our construction is the persistence of the domain of the Hamiltonian under the flow, obtained by the persistence of regularity method of Kato. We also identify a two-parameter family of distinct blow-up profiles, which should play a central role in the classification of non-radial minimal mass blow-up solutions on the star graph. Our construction is generic and can be extended to a star graph with an arbitrary number of edges. It can certainly also be adapted to other types of metric graphs.
ER -