Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

• 成果类型: Article
• 署名作者: Debussche, Arnaud; Liu, Ruoyuan; Tzvetkov, Nikolay; Visciglia, Nicola
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; University of Edinburgh; University of Edinburgh; Heriot Watt University; Ecole Normale Superieure de Lyon (ENS de LYON); University of Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01288-y
• 发表日期: 2024
• 页码: 1161-1218
• 关键词: schrodinger-equation; cauchy-problem; besov

摘要

We consider the nonlinear Schr & ouml;dinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labb & eacute; (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147-1174, 2019) with a sub-quadratic nonlinearity.