On strong convergence to 3D steady vortex sheets
On strong convergence to 3D steady vortex sheets
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DOI：
10.1016/j.jde.2007.05.008
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发表时间：
2007-08
影响因子：
2.4
通讯作者：
Q. Jiu;Z. Xin
中科院分区：
文献类型：
--
作者：
Q. Jiu;Z. Xin
本文首先建立了三维定常不可压Euler方程近似解的强收敛准则。对于轴对称流动，在涡量为一号且在L1空间一致有界的假设下，得到了近似解在Lloc 2（R3）中强收敛的一个充要条件.进一步，对于单符号和L1有界涡量，证明了如果一系列近似解集中在（r，z）平面上的一个孤立点上，那么集中点既不会出现在靠近轴的区域（包括对称轴本身），也不会出现在远离轴的区域.最后，我们给出了一个利用Hill球涡强收敛于Lloc ~ 2（R ~ 3）的近似解的例子。
In this paper, we first establish a strong convergence criterion of approximate solutions for the 3D steady incompressible Euler equations. For axisymmetric flows, under the assumption that the vorticity is of one sign and uniformly bounded in L1space, we obtain a sufficient and necessary condition for the strong convergence in Lloc2(R3) of approximate solutions. Furthermore, for one-sign and L1-bounded vorticity, it is shown that if a sequence of approximate solutions concentrates at an isolated point in (r,z)-plane, then the concentration point can appear neither in the region near the axis (including the symmetry axis itself) nor in the region far away from the axis. Finally, we present an example of approximates solutions which converge strongly in Lloc2(R3) by using Hill's spherical vortex.