On the global existence for the Muskat problem
On the global existence for the Muskat problem
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DOI：
10.4171/jems/360
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发表时间：
2013-01-01
影响因子：
2.6
通讯作者：
Strain, Robert M.
中科院分区：
文献类型：
--
作者：
Constantin, Peter;Cordoba, Diego;Strain, Robert M.
Muskat问题模拟了两种不同密度的不可压缩非混相流体之间的界面动力学。在这项工作中，我们证明了三个结果。首先，我们以新的“对数”守恒定律(3)的形式证明了一个L-2(R)极大原理，该定律由方程(1)满足。我们的第二个结果证明了如果初始数据小于显式可计算常数（例如parallel to f parallel to(1)），则唯一强解的全局存在性。
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L-2(R) maximum principle, in the form of a new "log" conservation law (3) which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance parallel to f parallel to(1)