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Well-posedness of the Muskat problem with H2 initial data

Abstract: We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to equilibrium for small H2 perturbations of the rest state. For the one-phase Muskat problem, we prove local well-posedness for H2 initial data of arbitrary size. Finally, we show that solutions to the Muskat equations instantaneously become infinitely smooth. © 2015 Elsevier Inc.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Advances inMathematics 286 (2016) 32-104

Editorial: Elsevier

 Año de publicación: 2016

Nº de páginas: 73

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.aim.2015.08.026

ISSN: 0001-8708,1090-2082

Url de la publicación: https://doi.org/10.1016/j.aim.2015.08.026

Autores/as

CHENG, ARTHUR C. H.

SHKOLLER, STEVE