论文标题
广义schrödinger方程的奇异征税过程和分散效应
Singular Levy processes and dispersive effects of generalized Schrödinger equations
论文作者
论文摘要
我们介绍了Schrödinger-type方程的新模型，这些模型概括了标准NLS，并根据方向进行不同的分散体。我们的目的是根据传播的方向来理解分散性能，本着波导歧管的精神，但扩散是不同类型的地方。我们主要考虑标准的欧几里得空间和波导情况，但我们的参数很容易扩展到其他类型的歧管（例如产品空间）。我们的方法自然而然地统一了以前的几个结果。这些模型也是数学物理学（例如相对论字符串）的开创性作品中出现的一些概括。特别是，我们证明了波导歧管上的大数据散射$ \ mathbb {r}^d \ times \ mathbb {t} $，$ d \ geq 3 $。在我们的设置中，该结果可以视为\ cite {tv2，yyz2}的类似物，在\ cite {gswz}中调查的波导类似物。证明的关键要素是用于设置该模型的Morawetz型估计。
We introduce new models for Schrödinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to understand dispersive properties depending on the directions of propagation, in the spirit of waveguide manifolds, but where the diffusion is of different types. We mainly consider the standard Euclidean space and the waveguide case but our arguments extend easily to other types of manifolds (like product spaces). Our approach unifies in a natural way several previous results. Those models are also generalizations of some appearing in seminal works in mathematical physics, such as relativistic strings. In particular, we prove the large data scattering on waveguide manifolds $\mathbb{R}^d \times \mathbb{T}$, $d \geq 3$. This result can be regarded as the analogue of \cite{TV2, YYZ2} in our setting and the waveguide analogue investigated in \cite{GSWZ}. A key ingredient of the proof is a Morawetz-type estimate for the setting of this model.
