题目：Global Solutions of 3-D Navier-Stokes Equations with Small Unidirectional Derivative

报告人：刘彦麟 博士（北京师范大学） 

地点：宁静楼117室

时间：2021年6月4日（星期五） 13：50-14：50

摘要：We prove that the classical 3-D Navier-Stokes equations have a unique global Fujita-Kato solution  provided that the $H^{-\frac12,0}$ norm of  $\pa_3u_0$ is sufficiently small compared to some quantities of the initial data, which keep invariant under the natural scaling of N-S and dilating in the $x_3$ variable.  This result  provides some classes of large initial data which are large in Besov space $B^{-1}_{\infty,\infty}$ and can  generate unique global solutions to 3-D Navier-Stokes system. In particular, we extend the previous results in a series of works by Chemin, Gallagher, Ping Zhang et al. for initial data with a slow variable to multi-scales slow variable initial data.

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