Journal article
The Zero Surface Tension Limit of Two-Dimensional Interfacial Darcy Flow
Journal of mathematical fluid mechanics, v 16(1), pp 105-143
2014
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Abstract
We perform energy estimates for a sharp-interface model of two-dimensional, two-phase Darcy flow with surface tension. A proof of well-posedness of the initial value problem follows from these estimates. In general, the time of existence of these solutions will go to zero as the surface tension parameter vanishes. We then make two additional estimates, in the case that a stability condition is satisfied by the initial data: we make an additional energy estimate which is uniform in the surface tension parameter, and we make an estimate for the difference of two solutions with different values of the surface tension parameter. These additional estimates allow the zero surface tension limit to be taken, showing that solutions of the initial value problem in the absence of surface tension are the limit of solutions of the initial value problem with surface tension as surface tension vanishes.
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Details
- Title
- The Zero Surface Tension Limit of Two-Dimensional Interfacial Darcy Flow
- Creators
- David M. Ambrose - Drexel University
- Publication Details
- Journal of mathematical fluid mechanics, v 16(1), pp 105-143
- Publisher
- Springer Basel
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000336402400005
- Scopus ID
- 2-s2.0-84896374602
- Other Identifier
- 991019168398004721
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InCites Highlights
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- Web of Science research areas
- Mathematics, Applied
- Mechanics
- Physics, Fluids & Plasmas