【数学学院】On the critical one component regularity for 3-D Navier-Stokes system

报告题目：On the critical one component regularity for 3-D Navier-Stokes system

报告人：张平

报告人单位：中国科学院数学与系统科学研究院

报告时间：7月23日（周一）下午3:30-4:30

报告地点：数学学院西303报告厅

邀请人：张旭

Abstarct: 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.

来源链接：http://math.scu.edu.cn/info/1062/3574.htm