Strichartz estimates and global well-posedness of the cubic NLS on \(\mathbb{T}^2\) (Q6610999)
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scientific article; zbMATH DE number 7919006
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strichartz estimates and global well-posedness of the cubic NLS on \(\mathbb{T}^2\) |
scientific article; zbMATH DE number 7919006 |
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Strichartz estimates and global well-posedness of the cubic NLS on \(\mathbb{T}^2\) (English)
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26 September 2024
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In this papier, the authors prove a \(L^4\)-Strichartz estimate for the cubic nonlinear Schrödinger equation on the two-dimensional Torus \(\mathbb{T}^2\). This estimate improving Bourgain's result implies global well-posedness for the cubic nonlinear Schrödinger equation (which is \(L^2\) critical) in \(H^s(\mathbb{T}^2)\), for any \(s>0\) and all Cauchy data small in the scaling space \(L^2(\mathbb{T}^2)\). To achieve their goal, the authors develop a new geometric method based on a counting argument.
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nonlinear Schrödinger equation
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well-posedness
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