Volume 10, Issue Supplement 1, August 2003, Pages 12 - 27
The Cauchy Problem for the Nonlinear Schrödinger Equation on a Compact Manifold
Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov
Available Online 1 August 2003.
- 10.2991/jnmp.2003.10.s1.2How to use a DOI?
We discuss the wellposedness theory of the Cauchy problem for the nonlinear Schrödinger equation on compact Riemannian manifolds. New dispersive estimates on the linear Schrödinger group are used to get global existence in the energy space on arbirary surfaces and three-dimensional manifolds, generalizing earlier results by Bourgain on tori. On the other hand, on specific manifolds such as spheres, new instability phenomena are displayed, leading to some kind of illposednesss in higher dimensions.
- © 2006, the Authors. Published by Atlantis Press.
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- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Nicolas Burq AU - Patrick Gérard AU - Nikolay Tzvetkov PY - 2003 DA - 2003/08/01 TI - The Cauchy Problem for the Nonlinear Schrödinger Equation on a Compact Manifold JO - Journal of Nonlinear Mathematical Physics SP - 12 EP - 27 VL - 10 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2003.10.s1.2 DO - 10.2991/jnmp.2003.10.s1.2 ID - Burq2003 ER -