On the Muskat problem with viscosity jump: Global in time results
On the Muskat problem with viscosity jump: Global in time results
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DOI：
10.1016/j.aim.2019.01.017
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发表时间：
2019-03-17
影响因子：
1.7
通讯作者：
Strain, R. M.
中科院分区：
文献类型：
--
作者：
Gancedo, F.;Garcia-Juarez, E.;Strain, R. M.
Muskat问题模拟了两种不同特性的不可压缩不混溶流体在多孔介质中的过滤。在本文中，我们考虑两种不同的恒定密度和不同的恒定粘度的流体的二维和三维设置。在这种情况下，有关的轮廓方程是非局部的，不仅在发展系统中，而且在涡度振幅和自由界面之间的隐式关系。在其他额外的困难中，没有最大值原理可用于L-无穷大界面的振幅和斜率。我们证明了临界空间中中等大小初始稳定数据的全局时存在性结果。我们还增强了以前的方法，显示平滑（即时解析性），提高了3D中的介质尺寸常数，以及分析规范的急剧衰减率。发现的技术是双重的，给不适定在不稳定的情况下，非常低的经常解决方案。(C)2019爱思唯尔公司All rights reserved.
The Muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media. In this paper, we consider both the 2D and 3D setting of two fluids of different constant densities and different constant viscosities. In this situation, the related contour equations are non-local, not only in the evolution system, but also in the implicit relation between the amplitude of the vorticity and the free interface. Among other extra difficulties, no maximum principles are available for the amplitude and the slopes of the interface in L-infinity. We prove global in time existence results for medium size initial stable data in critical spaces. We also enhance previous methods by showing smoothing (instant analyticity), improving the medium size constant in 3D, together with sharp decay rates of analytic norms. The found technique is twofold, giving ill-posedness in unstable situations for very low regular solutions. (C) 2019 Elsevier Inc. All rights reserved.