Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds
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.
Received: April 2009; Revised: August 2009; Published: December 2009.
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