Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds

Takafumi Akahori

doi:10.3934/cpaa.2010.9.261

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2010, Volume 9, Issue 2: 261-280. Doi: 10.3934/cpaa.2010.9.261

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Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds

Takafumi Akahori^1,

1.
Graduate School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, 790-8577

Received: March 31, 2009

Revised: July 31, 2009

Published: February 2010

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Abstract

We consider the defocusing cubic nonlinear Schrödinger equation on two dimensional closed Riemannian manifolds. We prove global well-posedness below the energy class on manifolds satisfying some condition. The main ingredient for the proof is an application of the I-method introduced by Colliander, Keel, Staffilani, Takaoka and Tao.

Keywords:

Nonlinear Schrödinger equation on manifold,
Global well-posedness.

Mathematics Subject Classification: Primary: 35Q55, 35B60; Secondary: 58J99.

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