Global existence of solutions to Schrödinger equations on compact riemannian manifolds below H 1

Sijia Zhong

Bulletin de la Société Mathématique de France (2010)

  • Volume: 138, Issue: 4, page 583-613
  • ISSN: 0037-9484

Abstract

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In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. s < 1 , under some bilinear Strichartz assumption. We will find some s ˜ < 1 , such that the solution is global for s > s ˜ .

How to cite

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Zhong, Sijia. "Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^1$." Bulletin de la Société Mathématique de France 138.4 (2010): 583-613. <http://eudml.org/doc/272385>.

@article{Zhong2010,
abstract = {In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. $s&lt;1$, under some bilinear Strichartz assumption. We will find some $\tilde\{s\}&lt;1$, such that the solution is global for $s&gt;\tilde\{s\}$.},
author = {Zhong, Sijia},
journal = {Bulletin de la Société Mathématique de France},
keywords = {schrödinger equation; compact riemannian manifold; global; I-method},
language = {eng},
number = {4},
pages = {583-613},
publisher = {Société mathématique de France},
title = {Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^1$},
url = {http://eudml.org/doc/272385},
volume = {138},
year = {2010},
}

TY - JOUR
AU - Zhong, Sijia
TI - Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^1$
JO - Bulletin de la Société Mathématique de France
PY - 2010
PB - Société mathématique de France
VL - 138
IS - 4
SP - 583
EP - 613
AB - In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. $s&lt;1$, under some bilinear Strichartz assumption. We will find some $\tilde{s}&lt;1$, such that the solution is global for $s&gt;\tilde{s}$.
LA - eng
KW - schrödinger equation; compact riemannian manifold; global; I-method
UR - http://eudml.org/doc/272385
ER -

References

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