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Pré-Publication, Document De Travail Année : 2012

Schrodinger Equation on homogeneous trees

Résumé

Let T be a homogeneous tree and L the Laplace operator on T. We consider the semilinear Schrodinger equation associated to L with a power-like nonlinearity F of degree d. We first obtain dispersive estimates and Strichartz estimates with no admissibility conditions. We next deduce global well-posedness for small L2 data with no gauge invariance assumption on the nonlinearity F. On the other hand if F is gauge invariant, L2 conservation leads to global well-posedness for arbitrary L2 data. Notice that, in contrast with the Euclidean case, these global well-posedness results hold with no restriction on d > 1. We finally prove scattering for small L2 data, with no gauge invariance assumption.
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Dates et versions

hal-00698540 , version 1 (16-05-2012)
hal-00698540 , version 2 (23-10-2013)

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Alaa Jamal Eddine. Schrodinger Equation on homogeneous trees. 2012. ⟨hal-00698540v1⟩
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