American Institute of Mathematical Sciences

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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

Takafumi Akahori 1,

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

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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