Sharp Interface Limit for a Stokes/Allen–Cahn System View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-07

AUTHORS

Helmut Abels, Yuning Liu

ABSTRACT

We consider the sharp interface limit of a coupled Stokes/Allen–Cahn system, when a parameter ϵ>0 that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For sufficiently small times we prove convergence of the solutions of the Stokes/Allen–Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature equation with an additional convection term coupled to a two-phase Stokes system with an additional contribution to the stress tensor, which describes the capillary stress. To this end we construct a suitable approximation of the solution of the Stokes/Allen–Cahn system, using three levels of the terms in the formally matched asymptotic calculations, and estimate the difference with the aid of a suitable refinement of a spectral estimate of the linearized Allen–Cahn operator. Moreover, a careful treatment of the coupling terms is needed. More... »

PAGES

417-502

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-018-1220-x

DOI

http://dx.doi.org/10.1007/s00205-018-1220-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1100917330


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