中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
偏微分方程研讨班
报告人：Rui Jin（Shanghai Jiaotong Univerisity）
题 目： Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations.
时 间：2024.07.09（星期二）14:00-16:00
地 点：S813
摘 要：This talk concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we show 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. As a consequence, one derives that the Lions exponent is the sharp viscosity threshold for the uniqueness/non-uniqueness in law of Leray solutions.
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