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

被引：112
作者：
Castro, Angel [1 ]
Cordoba, Diego [1 ]
Fefferman, Charles [2 ]
Gancedo, Francisco [3 ]
Lopez-Fernandez, Maria [4 ]
机构：
[1] CSIC, Inst Ciencias Matemat, Madrid, Spain
[2] Princeton Univ, Princeton, NJ 08544 USA
[3] Univ Seville, Seville, Spain
[4] Univ Zurich, Inst Math, CH-8001 Zurich, Switzerland
来源：
ANNALS OF MATHEMATICS | 2012年 / 175卷 / 02期
基金：
美国国家科学基金会;
关键词：
HELE-SHAW; INTERFACE EVOLUTION; CONTOUR DYNAMICS; WELL-POSEDNESS; POROUS-MEDIUM; FLUIDS; FLOW;
D O I：
10.4007/annals.2012.175.2.9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：909 / 948
页数：40
相关论文
共 34 条
[11]   Interface evolution: the Hele-Shaw and Muskat problems [J].
Cordoba, Antonio ;
Cordoba, Diego ;
Gancedo, Francisco .
ANNALS OF MATHEMATICS, 2011, 173 (01) :477-542
[12]   Interface evolution: Water waves in 2-D [J].
Cordoba, Antonio ;
Cordoba, Diego ;
Gancedo, Francisco .
ADVANCES IN MATHEMATICS, 2010, 223 (01) :120-173
[13]   Note on interface dynamics for convection in porous media [J].
Cordoba, Diego ;
Gancedo, Francisco ;
Orive, Rafael .
PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (10-12) :1488-1497
[14]   Contour dynamics of incompressible 3-d fluids in a porous medium with different densities [J].
Cordoba, Diego ;
Gancedo, Francisco .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 273 (02) :445-471
[15]   Absence of Squirt Singularities for the Multi-Phase Muskat Problem [J].
Cordoba, Diego ;
Gancedo, Francisco .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 299 (02) :561-575
[16]   A Maximum Principle for the Muskat Problem for Fluids with Different Densities [J].
Cordoba, Diego ;
Gancedo, Francisco .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 286 (02) :681-696
[17]   CONTOUR DYNAMICS AND CONTOUR SURGERY - NUMERICAL ALGORITHMS FOR EXTENDED, HIGH-RESOLUTION MODELING OF VORTEX DYNAMICS IN TWO-DIMENSIONAL, INVISCID, INCOMPRESSIBLE FLOWS [J].
DRITSCHEL, DG .
COMPUTER PHYSICS REPORTS, 1989, 10 (03) :77-146
[18]  
ESCHER J., 2010, ARXIV10052511
[19]  
Escher J., 1997, ADV DIFFERENTIAL EQU, V2, P619, DOI DOI 10.2308/JMAR-51966
[20]   the Parabolicity of the Muskat Problem: Well-Posedness, Fingering, and Stability Results [J].
Escher, Joachim ;
Matioc, Bogdan-Vasile .
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2011, 30 (02) :193-218
1234