The Zero Surface Tension Limit of TwoDimensional

Authors: David M Ambrose

Publish Date: 2013/08/08

Volume: 16, Issue: 1, Pages: 105-143

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Abstract

We perform energy estimates for a sharpinterface model of twodimensional twophase Darcy flow with surface tension A proof of wellposedness 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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