Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations
Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations
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DOI：
10.1007/s00205-016-0980-4
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发表时间：
2016-03
影响因子：
2.5
通讯作者：
C. Lacave;N. Masmoudi
中科院分区：
文献类型：
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作者：
C. Lacave;N. Masmoudi
研究了理想不可压缩流体在多孔区域中运动的渐近性态。多孔介质由大小不同的包裹体组成，包裹体之间的距离不同，流体充满了多孔介质的外部。如果包含分布在单位正方形上，则渐近性态取决于何时趋于零的极限。如果，则极限运动不受多孔介质的扰动，即我们恢复了整个空间的欧拉解。如果相反，则流体不能穿透多孔区域，即极限速度验证了不可渗透正方形外部的欧拉方程。如果夹杂物分布在单元段上，则其行为取决于夹杂物的几何形状：它由与障碍物横向边界的几何形状相关的极限确定。如果，则在极限处感觉不到孔的存在，而如果该极限为零，则出现不可渗透的壁。因此，对于一个方向上的分布，临界距离取决于夹杂物的形状;特别是，它等于球。
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of sizeseparated by distancesand the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit ofwhengoes to zero. If, then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary,, then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit ofwhereis related to the geometry of the lateral boundaries of the obstacles. If, then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal tofor balls.