Uniqueness of martingale solutions for the stochastic nonlinear Schr\"odinger equation on 3d compact manifolds
Analysis of PDEs
2018-09-03 v1 Probability
Abstract
We prove pathwise uniqueness for solutions of the nonlinear Schr\"{o}dinger equation with conservative multiplicative noise on compact 3D manifolds. In particular, we generalize the result by Burq, G\'erard and Tzvetkov (N. Burq, P. G\'erard, and N. Tzvetkov. Strichartz inequalities and the nonlinear Schr\"{o}dinger equation on compact manifolds. American Journal of Mathematics, 126 (3):569--605, 2004) to the stochastic setting. The proof is based on deterministic and stochastic Strichartz estimates and the Littlewood-Paley decomposition.
Keywords
Cite
@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}
}