| Softcover ISBN: | 978-2-85629-996-8 |
| Product Code: | SMFMEM/182 |
| List Price: | $63.00 |
| AMS Member Price: | $50.40 |
| Softcover ISBN: | 978-2-85629-996-8 |
| Product Code: | SMFMEM/182 |
| List Price: | $63.00 |
| AMS Member Price: | $50.40 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 182; 2024; 107 ppMSC: Primary 35; 42; 58
The authors prove global Strichartz inequalities for the Schrödinger equation on a large class of asymptotically conical manifolds. They show first that the low frequency part of any solution of the homogeneous Schrödinger equation enjoys the same global Strichartz estimates as those on the Euclidean space of dimension at least 3.
The authors also show that the high energy part also satisfies global Strichartz estimates without loss of derivatives outside a compact set, even if the manifold has trapped geodesics but in a temperate sense. They then show that the full solution satisfies global space-time Strichartz estimates if the trapped set is empty or sufficiently filamentary, and they derive a scattering theory for the \(L^{2}\) critical nonlinear Schrödinger equation in this geometric framework.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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The authors prove global Strichartz inequalities for the Schrödinger equation on a large class of asymptotically conical manifolds. They show first that the low frequency part of any solution of the homogeneous Schrödinger equation enjoys the same global Strichartz estimates as those on the Euclidean space of dimension at least 3.
The authors also show that the high energy part also satisfies global Strichartz estimates without loss of derivatives outside a compact set, even if the manifold has trapped geodesics but in a temperate sense. They then show that the full solution satisfies global space-time Strichartz estimates if the trapped set is empty or sufficiently filamentary, and they derive a scattering theory for the \(L^{2}\) critical nonlinear Schrödinger equation in this geometric framework.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
