三维紧流形上随机非线性薛定谔方程鞅解的唯一性
偏微分方程分析
2018-09-03 v1 概率论
摘要
我们证明了紧3D流形上带保守乘性噪声的非线性薛定谔方程解的路径唯一性。特别地，我们将Burq、Gérard和Tzvetkov（N. Burq, P. Gérard, and N. Tzvetkov. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. American Journal of Mathematics, 126 (3):569--605, 2004）的结果推广到随机情形。证明基于确定性与随机Strichartz估计以及Littlewood-Paley分解。
引用
@article{arxiv.1808.10619,
title = {Uniqueness of martingale solutions for the stochastic nonlinear Schr\"odinger equation on 3d compact manifolds},
author = {Zdzislaw Brzezniak and Fabian Hornung and Lutz Weis},
journal= {arXiv preprint arXiv:1808.10619},
year = {2018}
}