Cahn–Hilliard–Navier–Stokes systems with moving contact lines

We consider a well-known diffuse interface model for the study of the evolution of an incompressible binary fluid flow in a two or three-dimensional bounded domain. This model consists of a system of two evolution equations, namely, the incompressible Navier-Stokes equations for the average fluid ve...

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Veröffentlicht in:Calculus of variations and partial differential equations 2016-06, Vol.55 (3), p.1-47, Article 50
Hauptverfasser: Gal, C. G., Grasselli, M., Miranville, A.
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Sprache:eng
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Zusammenfassung:We consider a well-known diffuse interface model for the study of the evolution of an incompressible binary fluid flow in a two or three-dimensional bounded domain. This model consists of a system of two evolution equations, namely, the incompressible Navier-Stokes equations for the average fluid velocity u coupled with a convective Cahn–Hilliard equation for an order parameter ϕ . The novelty is that the system is endowed with boundary conditions which account for a moving contact line slip velocity. The existence of a suitable global energy solution is proven and the convergence of any such solution to a single equilibrium is also established.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-016-0992-9