具有一般粘性的二维多相Muskat问题
The multiphase Muskat problem with general viscosities in two dimensions
摘要：
本文研究了重力作用下垂直均匀多孔介质中三种具有一般粘度的不混溶流体运动的二维多相Muskat问题。采用Rellich类型的身份在该政权的流体是根据其粘度，分别是一个诺依曼系列参数时，流体是不有序的粘度，我们可以重铸的控制方程作为一个强耦合的非线性和非局部演化问题的函数parameterized分离的流体尖锐的接口。如果在每个界面上都满足Rayleigh-Taylor条件，则该问题是抛物型的。基于这一性质，我们证明了多相Muskat问题在所有的$L_2$ -亚临界索伯列夫空间中是适定的，并且它具有一些抛物光滑性质.
英文摘要：
In this paper we study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with general viscosities in a vertical homogeneous porous medium under the influence of gravity. Employing Rellich type identities in the regime where the fluids are ordered according to their viscosities, respectively a Neumann series argument when the fluids are not ordered by viscosity, we may recast the governing equations as a strongly coupled nonlinear and nonlocal evolution problem for the functions that parameterize the sharp interfaces that separate the fluids. This problem is of parabolic type if the Rayleigh-Taylor condition is satisfied at each interface. Based on this property, we then show that the multiphase Muskat problem is well-posed in all $L_2$-subcritical Sobolev spaces and that it features some parabolic smoothing properties.
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