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The Zero Surface Tension Limit of Two-Dimensional Interfacial Darcy Flow
Journal article   Peer reviewed

The Zero Surface Tension Limit of Two-Dimensional Interfacial Darcy Flow

David M. Ambrose
Journal of mathematical fluid mechanics, v 16(1), pp 105-143
2014

Abstract

Article Classical and Continuum Physics Fluid- and Aerodynamics Mathematical Methods in Physics Physics Physics and Astronomy
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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Web of Science research areas
Mathematics, Applied
Mechanics
Physics, Fluids & Plasmas
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