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arXiv · 1509.01952

On the critical one component regularity for 3-D Navier-Stokes system: general case

Jean-Yves Chemin·Ping Zhang·Zhifei Zhang
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Abstract

Let us consider an initial data $v_0$ for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to $L^{\frac 32}\cap L^2$. We prove that if the solution associated with $v_0$ blows up at a finite time $T^\star$, then for any $p$ in $]4,\infty[$, and any unit vector $e$ of $\R^3$, the $L^p$ norm in time with value in $\dot{H}^{\frac 12+\frac 2 p }$ of $(v|e)_{\R^3}$ blows up at $T^\star$

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Jean-Yves Chemin, Ping Zhang, Zhifei Zhang. 2015-09-07. On the critical one component regularity for 3-D Navier-Stokes system: general case. https://arxiv.org/abs/1509.01952

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