Well-posedness of the Muskat problem with H2 initial data
Well-posedness of the Muskat problem with H2 initial data
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DOI：
10.1016/j.aim.2015.08.026
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发表时间：
2016-01-02
影响因子：
1.7
通讯作者：
Shkoller, Steve
中科院分区：
文献类型：
--
作者：
Cheng, C. H. Arthur;Granero-Belinchon, Rafael;Shkoller, Steve
本文研究了二维多孔介质中两种不可压缩流体界面的动力学行为，其流动由Muskat方程模拟。对于两相Muskat问题，我们建立了全局适定性和衰减到平衡的小H-2扰动的休息状态。对于单相Muskat问题，我们证明了任意大小的H-2初始数据的局部适定性。最后，我们表明，解决方案的Muskat方程瞬间变得无限光滑。(C)2015 Elsevier Inc. All rights reserved.
We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to equilibrium for small H-2 perturbations of the rest state. For the one-phase Muskat problem, we prove local well-posedness for H-2 initial data of arbitrary size. Finally, we show that solutions to the Muskat equations instantaneously become infinitely smooth. (C) 2015 Elsevier Inc. All rights reserved.