ON A ROUGH PERTURBATION OF THE NAVIER-STOKES SYSTEM AND ITS VORTICITY FORMULATION

• 成果类型: Article
• 署名作者: Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein
• 署名单位: University of Bielefeld; Imperial College London; University of Agder
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1603
• 发表日期: 2021
• 页码: 736-777
• 关键词: equations; transport

摘要

We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous random dynamical system. In dimension three, the noise is not enstrophy balanced, and we establish the existence of local in time solutions.