论文标题
分数NLS的全球适应性和长期行为
Global well-posedness and long-time behavior of the fractional NLS
论文作者
论文摘要
在本文中，我们的讨论主要集中于具有能量超临界非线性的方程式。我们在各个维度上都建立了CubicSchrödinger方程的概率全球体能力（GWP）结果。我们考虑在径向环境中的低规律性和高规律性，在尺寸$ \ geq 2 $中。在高规律性的结果中，使用{\ it Indiscid -Indiscid -Indistional（IID）限制}，而在较低的规律性全局良好的结果中，我们使用Skorokhod表示定理。 IID极限作为一种独立方法列出，该方法适用于广泛的哈密顿PDE。此外，我们在任何维度上讨论了对周期性设置的适应，以进行平滑规律。
In this paper, our discussion mainly focuses on equations with energy supercritical nonlinearities. We establish probabilistic global well-posedness (GWP) results for the cubic Schrödinger equation with any fractional power of the Laplacian in all dimensions. We consider both low and high regularities in the radial setting, in dimension $\geq 2$. In the high regularity result, an {\it Inviscid - Infinite dimensional (IID) limit} is employed while in the low regularity global well-posedness result, we make use of the Skorokhod representation theorem. The IID limit is presented in details as an independent approach that applies to a wide range of Hamiltonian PDEs. Moreover we discuss the adaptation to the periodic settings, in any dimension, for smooth regularities.
