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

页码：909 / 948

页数：40

共 34 条

[1] Well-posedness of two-phase Hele-Shaw flow without surface tension [J].