Schrodinger Equation on homogeneous trees

Alaa Jamal Eddine

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arXiv · 1206.0835

Schrodinger Equation on homogeneous trees

Alaa Jamal Eddine

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Abstract

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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Alaa Jamal Eddine. 2013-10-23. Schrodinger Equation on homogeneous trees. https://arxiv.org/abs/1206.0835

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