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On an asymptotic model for free boundary Darcy flow in porous media

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arxiv 1810.11798 v2 pith:AXLAMPFA submitted 2018-10-28 math.AP

Rafael Granero-Belinchón , Stefano Scrobogna This is my paper · ORCID
classification math.AP
keywords asymptoticboundarydarcyflowfreemodelamplitudeapproximation
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We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces. Furthermore, we also study how the solution decays towards the flat equilibrium.

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  1. On a thin film model with insoluble surfactant

    math.AP 2019-08 conditional novelty 6.0 of 10

    Global weak solutions and exponential decay to the flat equilibrium are shown for the full thin film surfactant system with gravity, capillary, and van der Waals forces under explicit smallness conditions in Wiener algebras.

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