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Splash singularities for the one-phase Muskat problem in stable regimes

Opened Access Splash singularities for the one-phase Muskat problem in stable regimes

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Autor: Castro Martínez, Ángel
Córdoba Gazolaz, Diego
Fefferman, Charles L.
Gancedo García, Francisco
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2016-10
Publicado en: Archive for Rational Mechanics and Analysis, 222 (1), 213-243.
Tipo de documento: Artículo
Resumen: This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is with a dry region, where the density and the viscosity are set equal to 0 (the gradient of the pressure is equal to (0, 0)) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.
Cita: Castro Martínez, Á., Córdoba Gazolaz, D., Fefferman, C.L. y Gancedo García, F. (2016). Splash singularities for the one-phase Muskat problem in stable regimes. Archive for Rational Mechanics and Analysis, 222 (1), 213-243.
Tamaño: 365.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/45318

DOI: 10.1007/s00205-016-0999-6

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