Note on the flux condition and pressure drop in the resolvent problem of the Stokes system
Note on the flux condition and pressure drop in the resolvent problem of the Stokes system
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关于斯托克斯系统求解问题中的通量条件和压降的说明
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Farwig
中科院分区：
文献类型：
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作者：
R. Farwig
在[4] H. Sohr和作者考虑了孔径域中广义Stokes系统预解问题的Lq-理论。这种类型的无界域由两个不相交的半空间组成，这两个半空间彼此被一个壁分开，但通过该壁中的孔（孔径）连接。由于这种几何形状，通过孔的速度场的通量和无穷远处的压降是重要的物理量和数学量。在本文中，我们表明，为了挑选出一个独特的解决方案的预解问题，我们必须规定的流量为largeq，但对于smallq的流量和压降都不能规定。只有当维数大于2时，q的值才有一定的范围，在这个范围内，我们必须指定通量或压降。作为极限情形，我们还研究了Stokes系统的强解。
In [4] H. Sohr and the author considered theLq-theory of the resolvent problem of the generalized Stokes system in an aperture domain. This type of unbounded domain consists of two disjoint half spaces which are separated from each other by a wall but connected by a hole (aperture) in this wall. Due to this geometry the flux of the velocity field through the hole and the pressure drop at infinity are important physical and mathematical quantities. In this note we show that in order to single out a unique solution of the resolvent problem we must prescribe the flux for largeq, but that for smallq neither the flux nor the pressure drop can be prescribed. Only if the dimension is greater than two there is a certain range of values ofq where we must prescribe either the flux or the pressure drop. As a limit case we also investigate strong solutions of the Stokes system.