Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data

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URI: https://hdl.handle.net/10902/29584
ISSN: 0951-7715
ISSN: 1361-6544
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Autoría
Alonso Orán, Diego; Granero Belinchón, RafaelAutoridad Unican
Fecha
2022-08-16
Derechos
© IOP Publishing Ltd & London Mathematical Society. This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/ac803e
Publicado en
Nonlinearity, 2022, 35, 4749-4778
Editorial
Institute of Physics
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Palabras clave
Free Boundary
Porous Medium
Incompressible Flow
Global Existence
Maximum Principle
Resumen/Abstract
In this work we study the inhomogeneous Muskat problem, i.e. the evolution of an internal wave between two different fluids in a porous medium with discontinuous permeability. In particular, under precise conditions on the initial datum and the physical quantities of the problem, our results ensure the decay of the solutions towards the equilibrium state in the Lipschitz norm. In addition, we establish the global existence and decay of Lipschitz solutions.
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