Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations
Elia Bru\'eRui JinYachun LiDeng Zhang
Elia Bru\'eRui JinYachun LiDeng Zhang
Sep 2023
0被引用
0笔记
开学季活动火爆进行中，iPad、蓝牙耳机、拍立得、键盘鼠标套装等你来拿
摘要原文
This paper concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we prove that there exist distinct Leray solutions in the probabilistically weak sense. In particular, the joint uniqueness in law fails in the Leray class. The non-uniqueness also displays in the probabilistically strong sense in the local time regime, up to stopping times. Furthermore, we discuss the optimality from two different perspectives: sharpness of the hyper-viscous exponent and size of the external force. These results in particular yield that the Lions exponent is the sharp viscosity threshold for the uniqueness/non-uniqueness in law of Leray solutions. Our proof utilizes the self-similarity and instability programme developed by Jia \v{S}ver\'{a}k [42,43] and Albritton-Bru\'{e}-Colombo [1], together with the theory of martingale solutions including stability for non-metric spaces and gluing procedure.
