Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise

• 成果类型: Article
• 署名作者: Hofmanova, Martina; Lange, Theresa; Pappalettera, Umberto
• 署名单位: University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01233-5
• 发表日期: 2024
• 页码: 1183-1255
• 关键词: conjecture; FLOWS

摘要

We construct Holder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Holder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow transformation reducing the SPDE under investigation to a random PDE, and convex integration techniques introduced in the deterministic setting by De Lellis and Szekelyhidi, here adapted to consider the stochastic case. In particular, our novel approach allows to construct probabilistically strong solutions on [0,infinity) directly.