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

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March 2010, 9(2): 261-280. doi: 10.3934/cpaa.2010.9.261

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

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

Received April 2009 Revised August 2009 Published December 2009

Abstract
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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: Global well-posedness., Nonlinear Schrödinger equation on manifold.

Mathematics Subject Classification: Primary: 35Q55, 35B60; Secondary: 58J9.

Citation: Takafumi Akahori. Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure & Applied Analysis, 2010, 9 (2) : 261-280. doi: 10.3934/cpaa.2010.9.261

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