CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE
CUSP DEVELOPMENT IN HELE-SHAW FLOW WITH A FREE-SURFACE
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DOI：
10.1137/0146003
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发表时间：
1986-02-01
影响因子：
1.9
通讯作者：
HOWISON, SD
中科院分区：
文献类型：
--
作者：
HOWISON, SD
研究了Hele-Shaw单元的自由表面流动。一段时间以来，人们已经知道，当流体区域收缩时，会发生有限时间的爆炸，在自由表面形成一个尖点；在爆炸时间之后，解就不存在了。文中还列举了这种爆破的例子，以及一种新的过程，在这种过程中，在自由表面上形成一种不同类型的尖，但在此之后解继续存在。在对因变量（压力）进行变换后，新的尖点与“障碍”问题自由边界上的允许奇异点有关。
Free surface flow in a Hele–Shaw cell is considered. It has been known for some time that when the fluid region is contracting, a finite time blow-up can occur, in which a cusp forms in the free surface; the solution does not exist beyond the time of blow-up. Examples are presented of this blow-up, and also of a new process in which a cusp of a different type forms in the free surface, but after which the solution continues to exist. After a transformation of the dependent variable (the pressure) the new cusps are related to permissible singularities in the free boundary of the “obstacle” problem.