Repositorio de producción científica de la Universidad de Sevilla

On the global existence for the Muskat problem

 

Advanced Search
 
Opened Access On the global existence for the Muskat problem
Cites

Show item statistics
Icon
Export to
Author: Constantin, Peter
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Strain, Robert M.
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2013
Published in: Journal of the European Mathematical Society, 15 (1), 201-227.
Document type: Article
Abstract: The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new ``log'' conservation law (???) which is satisfied by the equation (???) for the interface. Our second result is a proof of global existence of Lipschitz continuous solutions for initial data that satisfy ∥f0∥L∞<∞ and ∥∂xf0∥L∞<1. We take advantage of the fact that the bound ∥∂xf0∥L∞<1 is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law. Lastly, we prove a global existence result for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance ∥f∥1≤1/5. Previous results of this sort used a small constant ϵ≪1 which was not explicit.
Cite: Constantin, P., Córdoba Gazolaz, D., Gancedo García, F. y Strain, R.M. (2013). On the global existence for the Muskat problem. Journal of the European Mathematical Society, 15 (1), 201-227.
Size: 232.2Kb
Format: PDF

URI: http://hdl.handle.net/11441/45145

DOI: 10.4171/JEMS/360

See editor´s version

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)