报 告 人：Ping Zhang (Academy of Mathematicsand Systems Science, Chinese Academy of Sciences)

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

报告时间：2018年4月26日17:00-18:00

报告地点：知新楼B-1238

报告摘要：

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 tothe Sobolev space $H^{\frac12}$), we prove that the solution $v$ given by theclassical Fujita-Katotheorem blows up in a finite time $T^\star$   only if, for any $p$ in $ ]4,6[$ and anyunit vector $e$ in $\R^3,$ there holds $\int_0^{T^\star}\|v(t)\cdote\|_{\dH^{\f12+\f2p}}^p\,dt=\infty.$ We remark that all these quantities arescaling invariant under the scaling transformation of Navier-Stokes system.

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