Almost sure well-posedness for the cubic nonlinear Schr\"{o}dinger equation in the super-critical regime on $\TTT^d$, $d\geq 3$

Haitian Yue

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arXiv · 1808.00657

Almost sure well-posedness for the cubic nonlinear Schr\"{o}dinger equation in the super-critical regime on $\TTT^d$, $d\geq 3$

Haitian Yue

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Abstract

In this paper we prove almost sure local well-posedness in both atomic spaces $X^s$ and Fourier restriction spaces $X^{s, b}$ for the cubic nonlinear Schr\"odinger equation on $\TTT^d$ ($d\geq 3$) in the super-critical regime.

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Haitian Yue. 2018-08-02. Almost sure well-posedness for the cubic nonlinear Schr\"{o}dinger equation in the super-critical regime on $\TTT^d$, $d\geq 3$. https://arxiv.org/abs/1808.00657

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