Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise

• 成果类型: Article
• 署名作者: Debussche, Arnaud; 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/s00440-013-0490-3
• 发表日期: 2014
• 页码: 575-596
• 关键词: markov solutions; stationary solutions; Absolute continuity; ergodicity; martingale; selections; REGULARITY

摘要

We prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic Navier-Stokes equations in dimension . In particular, under very mild assumptions on the noise, we prove that finite dimensional projections of the solutions have densities with respect to the Lebesgue measure which have some smoothness when measured in a Besov space. This is proved thanks to a new argument inspired by an idea introduced in (Fournier and Printems. Bernoulli 16(2):343-360, 2010).