Global sharp interface limit of the Hele–Shaw–Cahn–Hilliard system |
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| Authors: | Mingwen Fei |
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| Affiliation: | School of Mathematics and Computer Sciences, Anhui Normal University, Wuhu, China |
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| Abstract: | In this paper, we focus on a diffuse interface model named by Hele–Shaw–Cahn–Hilliard system, which describes a two‐phase Hele–Shaw flow with matched densities and arbitrary viscosity contrast in a bounded domain. The diffuse interface thickness is measured by ? , and the mobility coefficient (the diffusional Peclet number) is ? α . We will prove rigorously that the global weak solutions of the Hele–Shaw–Cahn–Hilliard system converge to a varifold solution of the sharp interface model as ? →0 in the case of 0≤α < 1. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | Hele‐Shaw‐Cahn‐Hilliard system two phase flow sharp interface varifold |
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