Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits

• 成果类型: Article
• 署名作者: Butori, Federico; Flandoli, Franco; Luongo, Eliseo; Tahraoui, Yassine
• 署名单位: Scuola Normale Superiore di Pisa; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01471-3
• 发表日期: 2026-08
• 页码: 1127-1188
• 关键词: Young Measures; Transport Noise; Stretching Noise; passive scalars; magnetohydrodynamics; Navier-Stokes equations; EXISTENCE

摘要

In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which give additional information on the fluctuations and oscillations of solutions: we prove convergence to non-trivial Young measures satisfying limit PDEs with suitable diffusion terms. In the case of a passive vector field the background Vlasov equation adds completely new statistical information to the stochastic advection equation.