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

• 成果类型: Article
• 署名作者: Castro, Angel; Cordoba, Diego; Fefferman, Charles; Gancedo, Francisco; Lopez-Fernandez, Maria
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.2.9
• 发表日期: 2012
• 页码: 909-948
• 关键词: hele-shaw; interface evolution; contour dynamics; well-posedness; porous-medium; fluids; FLOW

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.