A minimal mass blow-up solution on a nonlinear quantum star graph
2023
Online
report
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 $N\ge 2$. 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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A minimal mass blow-up solution on a nonlinear quantum star graph
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Autor/in / Beteiligte Person: | Genoud, François ; Coz, Stefan Le ; Royer, Julien |
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Veröffentlichung: | 2023 |
Medientyp: | report |
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