Navier–Stokes equations: Green's matrices, vorticity direction, and regularity up to the boundary
Navier–Stokes equations: Green's matrices, vorticity direction, and regularity up to the boundary
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DOI：
10.1016/j.jde.2008.02.043
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发表时间：
2009-01
影响因子：
2.4
通讯作者：
H. B. Veiga;L. Berselli
中科院分区：
文献类型：
--
作者：
H. B. Veiga;L. Berselli
考虑三维Navier-Stokes方程的初边值问题。物理域是一个有界开集与光滑的边界上，我们假设一个条件的自由边界类型。我们表明，如果一个适当的假设涡度方向，那么弱解是正规的。我们在证明中使用的主要工具是通过绿色矩阵，用涡量来表示速度的显式表达式。
We consider the initial–boundary value problem for the 3D Navier–Stokes equations. The physical domain is a bounded open set with a smooth boundary on which we assume a condition of free-boundary type. We show that if a suitable hypothesis on the vorticity direction is assumed, then weak solutions are regular. The main tool we use in the proof is an explicit representation of the velocity in terms of the vorticity, by means of Green's matrices.