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

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

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