报告题目: Global solutions of 3-D Navier-Stokes system with small unidirectional derivative
报告人: 刘彦麟(北京师范大学)
报告地点:管研楼1418
报告时间:
14:00-15:00, 09-03, 2020 (北京时间)
摘要:
In this talk, we prove that the classical 3-D Navier-Stokes system has a unique global Fujita-Kato solution, provided that the $H^{-\frac 12,0}$ norm of $\partial_3 u_0$ is sufficiently small compared to some scaling invariant quantities of the initial data, and these quantities keeps invariant under dilation in $x_3$ variable. This result provides some classes of large initial data which are large in Besov space $B^{-1}_{\infty,\infty}$ and still can generate unique global solution to 3-D Navier-Stokes system. In particular, we extend the previous results in a series of works by Chemin, Gallagher et al for initial data with a slow variable to multi-scales slow variable initial data. At last we will generalize this result to anisotropic Navier-Stokes system with only horizontal dissipation by a different approach. This is a joint work with Ping Zhang and Marius Paicu.