GLOBAL WELL POSEDNESS OF THE TWO-DIMENSIONAL STOCHASTIC NONLINEAR WAVE EQUATION ON AN UNBOUNDED DOMAIN

• 成果类型: Article
• 署名作者: Tolomeo, Leonardo
• 署名单位: University of Bonn
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1484
• 发表日期: 2021
• 页码: 1402-1426
• 关键词: data cauchy-theory; schrodinger-equation

摘要

We study the two-dimensional wave equation with cubic nonlinearity posed on R-2 with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for initial data in H-s, s > 4/5.