On the critical one component regularity for 3-D Navier-Stokes system
[TMCSC]
July 23, 2018 15:30-16:30
W303 School of Mathematics, Sichuan University
![[lecture]Ping Zhang0723-01.png](http://tianyuan.scu.edu.cn/upload/default/20180720/%5Blecture%5DPing%20Zhang0723-01.png "[lecture]Ping Zhang0723-01.png")
SPEAKERS
张平（中国科学院数学与系统科学研究院）
ABSTRACT
Given an initial data $v_0$ with vorticity~$\Om_0=\na\times v_0$ in~$L^{\frac 3 2}, $ (which implies that~$v_0$ belongs to the Sobolev space~$H^{\frac12}$), we prove that the solution~$v$ given by the classical Fujita-Kato theorem blows up in a finite time~$T^\star$ only if, for any $p$ in~$ ]4, 6[$ and any unit vector~$e$ in~$\R^3, $ there holds $ \int_0^{T^\star}\|v(t)\cdot e\|_{\dH^{\f12+\f2p}}^p\,dt=\infty.$ We remark that all these quantities are scaling invariant under the scaling transformation of Navier-Stokes system.
ORGANIZERS
Hui Kou (Sichuan University)
Xu Zhang (Sichuan University)
Jie Zhou (Sichuan University)
SUPPORTED BY
Tianyuan Mathematical Center in Southwest China
School of Mathematics, Sichuan University
VIDEO
- On the critical one component regularity for 3-D Navier-Stokes system
- 15:30 - 16:30, 2018-07-23
- 张平（中国科学院数学与系统科学研究院）