Journal of Nonlinear Mathematical Physics

Volume 10, Issue Supplement 1, August 2003, Pages 12 - 27

The Cauchy Problem for the Nonlinear Schrödinger Equation on a Compact Manifold

Authors
Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov
Corresponding Author
Nicolas Burq
Available Online 1 August 2003.
DOI
https://doi.org/10.2991/jnmp.2003.10.s1.2How to use a DOI?
Abstract
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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - Supplement 1
Pages
12 - 27
Publication Date
2003/08/01
ISBN
91-631-4340-2
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2003.10.s1.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

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  - https://doi.org/10.2991/jnmp.2003.10.s1.2
ID  - Burq2003
ER  -