论文标题
多相马斯卡特问题与一般粘度二维的一般粘度
The multiphase Muskat problem with general viscosities in two dimensions
论文作者
论文摘要
在本文中，我们研究了二维多相麝香问题，描述了在重力影响下在垂直均匀的多孔培养基中具有一般粘度的三种不混溶性流体的运动。在该方案中采用Rellich类型的身份，该状态根据其粘度进行排序，分别是Neumann系列的参数，当流体未通过粘度订购时，我们可能会将管理方程式重塑为强烈耦合的非线性和非局部进化问题，以使锋利的函数分开尖锐的杂物，从而分离出锋利的杂物。如果在每个接口上满足雷利 - 泰勒条件，则此问题是抛物线类型。然后，基于此属性，我们表明多相麝香问题在所有$ l_2 $ subiubclitical sobolev空间中都有良好的含量，并且具有一些抛物线平滑属性。
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.
