Cordoba Antonio, Cordoba Diego, Gancedo Francisco
Department of Mathematics, Universidad Autonoma de Madrid, Carretera de Colmenar Viejo, Km. 15, 28049 Madrid, Spain.
Proc Natl Acad Sci U S A. 2009 Jul 7;106(27):10955-9. doi: 10.1073/pnas.0809874106. Epub 2009 Jun 24.
For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different because it emphasizes the active scalar character of the system and does not require the presence of gravity.
对于两相Hele-Shaw和Muskat问题的自由边界动力学，以及对于无旋不可压缩Euler方程，当二维界面最初满足瑞利 - 泰勒条件时，我们证明了局部时间内的存在性。水波的结果最初是由吴在一个略有不同的情形（在无穷远处消失）中得到的，但我们的方法不同，因为它强调了系统的有源标量特性，并且不需要重力的存在。
