## 博士生论坛

### 学术报告：On the critical one component regularity for 3-D Navier-Stokes system

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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