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Pré-Publication, Document De Travail Année : 2023

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

Résumé

The main contribution of this article is the construction of a finite time blow-up solution to the mass-critical focusing nonlinear Schr\"odinger equation set on a metric star graph $\mathcal G$ with $N$ edges, for any $N \geq 2$. After establishing well-posedness of the corresponding Cauchy problem in $H^1(\mathcal G)$, we obtain the sharp threshold for global existence in terms of the mass of the ground state, called minimal mass. We then construct a minimal mass solution which blows up in finite time at the vertex of $\mathcal G$. The blow-up profile and blow-up speed are characterized explicitly.
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Dates et versions

hal-04045570 , version 1 (24-03-2023)

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François Genoud, Stefan Le Coz, Julien Royer. A minimal mass blow-up solution on a nonlinear quantum star graph. 2023. ⟨hal-04045570⟩
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