The Schrodinger equation with spatial white noise potential

被引：21

作者：

Debussche, Arnaud ^{[1
]}

Weber, Hendrik ^{[2
]}

机构：

[1] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

[2] Univ Warwick, Coventry, W Midlands, England

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2018年 / 23卷

基金：

美国国家科学基金会;

关键词：

nonlinear Schrodinger equation; spatial white noise; renormalization;

D O I：

10.1214/18-EJP143

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the linear and nonlinear Schrodinger equation with a spatial white noise as a potential over the two dimensional torus. We prove existence and uniqueness of solutions to an initial value problem for suitable initial data. Our construction is based on a change of unknown originally used in [13] and conserved quantities.

引用

页数：16

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