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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 3, 2014, pp. 271–288
DOI: 10.4171/ZAA/1511

Published online: 2014-07-02

Regularity Results for a Cahn-Hilliard-Navier-Stokes System with Shear Dependent Viscosity

Maurizio Grasselli[1] and Dalibor Pražák[2]

(1) Politecnico di Milano, Italy
(2) Charles University, Prague, Czech Republic

We analyze a di ffuse interface model describing the behavior of a mixture of two incompressible fluids. More precisely, we consider Navier-Stokes type equations with power-law like shear dependent viscosity. Such equations are nonlinearly coupled with a convective Cahn-Hilliard equation for the order parameter. The resulting system is endowed with no-slip and no-flux boundary conditions. We prove some regularity properties of weak solutions under rather general conditions. This is a generalization of previous results already proven for single fluids. Some consequences of such results are also addressed.

Keywords: Incompressible viscous fluids, shear dependent viscosity, binary mixtures, diffuse interfaces, Cahn-Hilliard equations, regularity of solutions

Grasselli Maurizio, Pražák Dalibor: Regularity Results for a Cahn-Hilliard-Navier-Stokes System with Shear Dependent Viscosity. Z. Anal. Anwend. 33 (2014), 271-288. doi: 10.4171/ZAA/1511