Geodesic
Local solvability and turning for the inhomogeneous Muskat problem
Luigi C. Berselli1 ; Diego Córdoba2 ; Rafael Granero-Belinchón3
1Università di Pisa, Italy
2Universidad Autónoma de Madrid, Spain
3University of California at Davis, USA
Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 175-213

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DOI

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R2 or a bounded strip S=R×(−π/2,π/2). The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogeneus Muskat problem with infinite depth.
DOI : 10.4171/ifb/317
Classification : 35-XX
Mots-clés : Darcy’s law, inhomogeneous Muskat problem, well-posedness, blow-up, maximum principle

Luigi C. Berselli  1   ; Diego Córdoba  2   ; Rafael Granero-Belinchón  3

1 Università di Pisa, Italy
2 Universidad Autónoma de Madrid, Spain
3 University of California at Davis, USA 
Luigi C. Berselli; Diego Córdoba; Rafael Granero-Belinchón. Local solvability and turning for the inhomogeneous Muskat problem. Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 175-213. doi: 10.4171/ifb/317
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     title = {Local solvability and turning for the inhomogeneous {Muskat} problem},
     journal = {Interfaces and free boundaries},
     pages = {175--213},
     year = {2014},
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     number = {2},
     doi = {10.4171/ifb/317},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/317/}
}
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