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

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)