Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model

Volume 10, Issue 8, pp 4209--4221 http://dx.doi.org/10.22436/jnsa.010.08.16

Publication Date: August 16, 2017 Submission Date: June 05, 2017

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Authors

Kelong Cheng - School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China. Wenqiang Feng - Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, USA.

Abstract

The global well-posedness analysis for the three dimensional dynamic Cahn-Hilliard-Stokes (CHS) model is provided in this paper. In this model, the velocity vector is determined by the phase variable by both the Darcy law and the Stokes equation. Based on the analysis of weak solutions to the CHS equation by the standard Galerkin method, we present a global in time strong solution for the CHS model. Moreover, the existence and the uniqueness of the strong solution are also proven.

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Keywords

• Cahn-Hilliard-Stokes model
• Sobolev embedding
• Galerkin procedure
• Hemlholtz projection.

MSC

•  35K55
•  76D05

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