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引用次数: 18
摘要
研究了$\mathbb{R}^d$上随机初始数据低于临界正则性$H^{\frac{d-1}{2}}$的五次非线性Schr\ odinger方程。主要结果是给出$H^s$中$s \in (\frac{d-2}{2}， \frac{d-1}{2})$的数据的Wiener随机化，证明了几乎肯定的局部适定性。该论证进一步发展了A的工作中引入的技术。B 'enyi T. Oh和O. Pocovnicu关于三次问题。最后给出了几乎确定全局适定性的一个条件。
Almost sure local well-posedness for the supercritical quintic NLS
This paper studies the quintic nonlinear Schr\"odinger equation on $\mathbb{R}^d$ with randomized initial data below the critical regularity $H^{\frac{d-1}{2}}$. The main result is a proof of almost sure local well-posedness given a Wiener Randomization of the data in $H^s$ for $s \in (\frac{d-2}{2}, \frac{d-1}{2})$. The argument further develops the techniques introduced in the work of \'A. B\'enyi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.
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