论文标题
关于J.-L的Navier-Stokes方程法律的非唯一性的评论。狮子的指数
Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent
论文作者
论文摘要
狮子会（1959年，公牛。随后，他（1969年，Dunod，Gauthiers-Villars，Paris）声称其解决方案的独特性是当其指数不少于五个季度时，如果空间维度为三个。 Following the work of Hofmanov$\acute{\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]), we prove the non-uniqueness in law for the three-dimensional stochastic Navier-Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.
Lions (1959, Bull. Soc. Math. France, \textbf{87}, 245--273) introduced the Navier-Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanov$\acute{\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]), we prove the non-uniqueness in law for the three-dimensional stochastic Navier-Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.
