主讲人：张平 研究员（中科院数学与系统科学研究院）

时  间：2014年4月8日（周二）16:00-17:00

地  点：必赢76net线路官网北二区教学楼 517 教室

摘  要：Given an initial data $v_0$ with vorticity~$\Omega_0=\nabla\times v_0$ 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\|_{H^{\f12+\f2p}}^p\,dt=\infty.$ We remark that all these quantities are scaling invariant under the scaling transformation of Navier-Stokes system.