Uniqueness and blow-up for a stochastic viscous dyadic model

• 成果类型: Article
• 署名作者: Romito, Marco
• 署名单位: University of Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0499-7
• 发表日期: 2014
• 页码: 895-924
• 关键词: navier-stokes equations; markov solutions; finite-time; martingale problem; heat-equation; noise; ergodicity; DISSIPATION; selections

摘要

We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove pathwise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data.