Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

• Autores: Ángel Castro Vázquez, Diego Córdoba Gazolaz , Charles L. Fefferman , Francisco Gancedo García , María López Fernández
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 175, Nº 2, 2012, págs. 909-948
• Idioma: inglés
• DOI: 10.4007/annals.2012.175.2.9
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• Resumen

  • The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.