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Well-posedness of an asymptotic model for free boundary Darcy flow in porous media in the critical Sobolev space

Published 29 Sep 2020 in math.AP | (2009.14117v2)

Abstract: We prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow is well posed in $ \dot{H}{3/2} $, and globally well-posed if the initial datum is small in $ \dot{H}{3/2} $.

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