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- W4298175636 abstract "We prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schrodinger equation. Precisely we show that a unique and global solution exists for initial data in the Sobolev space $H^{s}(mathbb R)$ for any $s>{1/3}$. This improves the result in cite{tz}, where global well-posedness was established for any $s>{4/9}$. We use the $I$-method to take advantage of the conservation laws of the equation. The new ingredient in our proof is an interaction Morawetz estimate for the smoothed out solution $Iu$. As a byproduct of our proof we also obtain that the $H^{s}$ norm of the solution obeys polynomial-in-time bounds." @default.
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- W4298175636 date "2007-02-23" @default.
- W4298175636 modified "2023-10-01" @default.
- W4298175636 title "Global well-posedness and polynomial bounds for the defocusing $L^{2}$-critical nonlinear Schrodinger equation in $R$" @default.
- W4298175636 doi "https://doi.org/10.48550/arxiv.math/0702707" @default.
- W4298175636 hasPublicationYear "2007" @default.
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