On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on \(\mathbb {R}^d\), \(d \geq 3\) (Q2795833)
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scientific article; zbMATH DE number 6559561
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on \(\mathbb {R}^d\), \(d \geq 3\) |
scientific article; zbMATH DE number 6559561 |
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22 March 2016
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nonlinear Schrödinger equation
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almost sure well-posedness
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modulation space
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Wiener decomposition
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probabilistic Cauchy theory
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On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on \(\mathbb {R}^d\), \(d \geq 3\) (English)
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The authors study the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS): \(i\partial_t u+\bigtriangleup u=\pm| u|^2 u\) on \(\mathbb{R}^d\), \(d\geq 3\) with random initial data and prove almost sure well-posedness results below the scaling-critical regularity \(s_{\mathrm{crit}}=\frac{d-2}{2}\).
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