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

Pages: 261 - 280, Volume 9, Issue 2, March 2010

doi:10.3934/cpaa.2010.9.261       Abstract        Full Text (266.1K)       Related Articles

Takafumi Akahori - Graduate School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, 790-8577, Japan (email)

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.

Received: April 2009;      Revised: August 2009;      Published: December 2009.