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Strichartz estimates for long range perturbations

Jean-Marc Bouclet·Nikolay Tzvetkov
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Abstract

We study local in time Strichartz estimates for the Schroedinger equation associated to long range perturbations of the flat Laplacian on the euclidean space. We prove that in such a geometric situation, outside of a large ball centered at the origin, the solutions of the Schroedinger equation enjoy the same Strichartz estimates as in the non perturbed situation. The proof is based on the Isozaki-Kitada parametrix construction. If in addition the metric is non trapping, we prove that the Strichartz estimates hold in the whole space.

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Jean-Marc Bouclet, Nikolay Tzvetkov. 2006-11-21. Strichartz estimates for long range perturbations. https://arxiv.org/abs/math/0509489

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