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Almost Morawetz estimates and global well-posedness for the defocusing L2-critical nonlinear schrödinger equation in higher dimensions. arXiv:0909.4332v1 (0)

by B Dodson
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Global well-posedness and scattering for the defocusing L²-critical nonlinear Schrödinger equation when d = 1

by Benjamin Dodson , 2015
"... In this paper we prove global well- posedness and scattering for the defocusing, one dimensional mass- critical nonlinear Schrödinger equation. We make use of a long- time Strichartz estimate and a frequency localized Morawetz estimate. This continues work begun in [28] and [30] for dimensions d ≥ ..."
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In this paper we prove global well- posedness and scattering for the defocusing, one dimensional mass- critical nonlinear Schrödinger equation. We make use of a long- time Strichartz estimate and a frequency localized Morawetz estimate. This continues work begun in [28] and [30] for dimensions d ≥ 3 and d = 2 respectively.

Global well-posedness and scattering for the mass critical nonlinear Schrödinger . . .

by Benjamin Dodson , 2013
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by Benjamin Dodson , 2012
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by Benjamin Dodson , 2011
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...ince we are truncating to low frequencies, our method is very similar to the almost Morawetz estimates that are often used in conjunction with the I-method. (See [1], [8], [9], [10], [12], [6], [17], =-=[15]-=-, [13], and [14] for more information on the I-method.) We will also use the estimates in §§4− 5 in order to preculde the case (1.15) by proving additional regularity. This method is similar to the me...

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by Benjamin Dodson , 2011
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...ince we are truncating to low frequencies, our method is very similar to the almost Morawetz estimates that are often used in conjunction with the I-method. (See [1], [8], [9], [10], [12], [6], [19], =-=[15]-=-, [13], and [14] for more information on the I-method.) 2 Function Spaces and linear estimates Linear Strichartz Estimates: Definition 2.1 A pair (p, q) will be called an admissible pair for d = 1 if ...

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