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arXiv · 2009.14117

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

Stefano Scrobogna
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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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Stefano Scrobogna. 2021-02-08. Well-posedness of an asymptotic model for free boundary Darcy flow in porous media in the critical Sobolev space. https://arxiv.org/abs/2009.14117

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