Strichartz estimates for long range perturbations
By Jean-Marc Bouclet, Nikolay Tzvetkov. 2005
70 citations recorded by the source corpus.
We study local in time Strichartz estimates for the Schrödinger equation associated to long range perturbations of the flat Laplacian on the Euclidean space. We prove that in such a geometric situation, outside a large ball centered at the origin, the solutions of the Schrödinger equation enjoy the same Strichartz estimates as in the nonperturbed situation. The proof is based on the Isozaki-Kitada parametrix construction. If in addition the metric is nontrapping, we prove that the Strichartz estimates hold in the whole space.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/19ef0ed860d2dda6983e40423ea5130563341c62
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In Applied Mathematics
- D. Tataru
- Jason Metcalfe
- Terence Tao
- Hart F. Smith
- Christopher D. Sogge
- Jacob Sterbenz
- Carlos E. Kenig
- Herbert Koch
In Mathematical Physics
- D. Tataru
- Terence Tao
- Jason Metcalfe
- Carlos E. Kenig
- J. Krieger
- Jacob Sterbenz
- Hart F. Smith
- A. Ionescu
Citations in the corpus
- Parametrices and dispersive estimates for Schrödinger operators with variable coefficients (2008, background): “Assume that a is a real symbol in S(2), uniformly in t G [0, 1].”