# 09-03【刘彦麟】管楼1418 微分方程系列报告

14:00-15:00, 09-03, 2020 (北京时间)

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.