Journal article
Well-posedness of two-phase Hele–Shaw flow without surface tension
European journal of applied mathematics, v 15(5), pp 597-607
Oct 2004
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We prove short-time well-posedness of a Hele–Shaw system with two fluids and no surface tension (this is also known as the Muskat problem). We restrict our attention here to the stable case of the problem. That is, in order for the motion to be well-posed, the initial data must satisfy a sign condition which is a generalization of a condition of Saffman and Taylor. This sign condition essentially means that the more viscous fluid must displace the less viscous fluid. The proof uses the formulation introduced in the numerical work of Hou, Lowengrub, and Shelley, and relies on energy methods.
Metrics
Details
- Title
- Well-posedness of two-phase Hele–Shaw flow without surface tension
- Creators
- DAVID M. Ambrose - Courant Institute of Mathematical Sciences
- Publication Details
- European journal of applied mathematics, v 15(5), pp 597-607
- Publisher
- Cambridge University Press
- Number of pages
- 11
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000228058500005
- Scopus ID
- 2-s2.0-16644399272
- Other Identifier
- 991019295200404721
UN Sustainable Development Goals (SDGs)
This publication has contributed to the advancement of the following goals:
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied