Chaos expansion solutions of stochastic magnetic Schr\'odinger equations on curved spaces

Autor:	Coriasco, Sandro, Pilipović, Stevan, Seleši, Dora
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Probability 35L10 60H15 (Primary) 35L40 35S30 60G20 60H40 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We treat some classes of stochastic partial differential equations of Schr\"odinger type within the framework of white noise analysis, combined with Wiener-It\^o chaos expansions and pseudodifferential operator methods. The initial data and potential term of the Schr\"odinger operator are assumed to be generalized stochastic processes that have both temporal and spatial dependence. We prove that the equations under consideration have unique solutions in the appropriate (intersections of weighted) Sobolev-Kato-Kondratiev spaces. Comment: 18 pages. This is the first version. It is expected that some revisions will be performed in the future
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.00325 Zobrazit plný text záznamu View this record from Arxiv