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A minimal mass blow-up solution on a nonlinear quantum star graph

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arxiv 2302.09678 v2 pith:RYA5RNJV submitted 2023-02-19 math.AP

François Genoud , Stefan Le Coz , Julien Royer This is my paper · ORCID
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keywords blow-upmassgraphminimalsolutionstararbitraryconstruct
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We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schr\"odinger equation on a metric star graph with an arbitrary number of edges. We show that all solutions are global if their mass is smaller than an explicit constant, called "minimal mass". We then construct a solution with minimal mass and arbitrary energy, which blows up in finite time at the vertex of the star graph. The blow-up profile and blow-up speed are explicitly characterized. The main novelty of the paper is the construction of the blow-up profile in time-dependent domains of singularly perturbed Laplacians.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Transverse Instability and Bifurcation Analysis of the line soliton for the NLS equation on a Fractured Strip

    math.AP 2026-08 conditional novelty 7.0 of 10

    For NLS on a strip with an attractive delta interaction, line solitons are orbitally stable below a critical width and unstable above, with a pitchfork branch of new positive solutions at the threshold.

  2. Ground states on a fractured strip and one dimensional reduction

    math.AP 2024-11 conditional novelty 7.0 of 10

    Ground states of the nonlinear Schrödinger equation on a fractured strip converge, as the strip narrows, to the ground state of the 1-D equation with a delta potential.

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