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Interface evolution: the Hele-Shaw and Muskat problems

 

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Author: Córdoba Barba, Antonio
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2011
Published in: Annals of Mathematics, 173, 477-542.
Document type: Article
Abstract: We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy’s law. The free boundary is given by the discontinuity among the densities and viscosities of the fluids. This physical scenario is known as the two dimensional Muskat problem or the two-phase Hele-Shaw flow. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition.
Cite: Córdoba Barba, A., Córdoba Gazolaz, D. y Gancedo García, F. (2011). Interface evolution: the Hele-Shaw and Muskat problems.. Annals of Mathematics, 173, 477-542.
Size: 399.4Kb
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URI: http://hdl.handle.net/11441/45171

DOI: 10.4007/annals.2011.173.1.10

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