Global well-posedness for a periodic nonlinear Schrodinger equation in 1D and 2D

De Silva  D; Pavlovic  N; Staffilani  GTzirakis  N

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Global well-posedness for a periodic nonlinear Schrodinger equation in 1D and 2D

机译：Global well-posedness for a periodic nonlinear Schrodinger equation in 1D and 2D

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摘要

The initial value problem for the L-2 critical semilinear Schrodinger equation with periodic boundary data is considered. We show that the problem is globally well-posed in H-s(T-d), for s > 4/9 and s > 2/3 in 1D and 2D respectively, confirming in 2D a statement of Bourgain in 4. We use the "I-method". This method allows one to introduce a modification of the energy functional that is well defined for initial data below the H-1(T-d) threshold. The main ingredient in the proof is a "refinement" of the Strichartz's estimates that hold true for solutions defined on the rescaled space, T-lambda(d) = R-d/lambda Z(d), d = 1, 2.

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来源
《Discrete and continuous dynamical systems》 |2007年第1期|37-65|共29页
作者
De Silva D; Pavlovic N; Staffilani GTzirakis N;
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作者单位

Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA;

Princeton Univ, Dept Math, Princeton, NJ 08544 USA;

MIT, Dept Math, Cambridge, MA 02139 USAUniv Toronto, Dept Math, Toronto, ON M5S 2E4, Canada;

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正文语种英语
中图分类理论力学（一般力学）;
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global well-posedness; nonlinear dispersive equations; nonlinear Schrodinger equation; PARTIAL-DIFFERENTIAL-EQUATIONS; CAUCHY-PROBLEM; POINTS; NUMBER; FORMS; KDV; NLS;

Global well-posedness for a periodic nonlinear Schrodinger equation in 1D and 2D

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