Abstract
We study the dynamics of the interface between two incompressible 2D flows where the evolution equation is obtained from Darcy’s law. The free boundary is given by the discontinuity among the densities and viscosities of the fluids. This physical scenario is known as the twodimensional Muskat problem or the twophase HeleShaw flow. We prove localexistence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the RayleighTaylor condition.

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@article {Ambrose, MRKEY = {2128613},
AUTHOR = {Ambrose, David M.},
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