Geodesic
Longtime behavior of a diffuse interface model for binary fluid mixtures with shear dependent viscosity
Maurizio Grasselli1 orcid ; Dalibor Pražák2
1Politecnico di Milano, Italy
2Charles University, Prague, Czech Republic
Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 507-530

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DOI

We consider a system which describes the behavior of a binary mixture of immiscible incompressible fluids with shear dependent viscosity by means of the diffuse interface approach. This system consists of Navier–Stokes type equations, characterized by a nonlinear stress-strain law, which are nonlinearly coupled with a convective Cahn–Hilliard equation for the order parameter. We analyze the corresponding dynamical system and, by means of the short trajectory method, we prove the existence of global and exponential attractors. We also discuss the dependence of an upper bound of the fractal dimension on the physical parameters of the system.
DOI : 10.4171/ifb/270
Classification : 35-XX, 76-XX, 00-XX
Mots-clés : Incompressible viscous fluids; shear dependent viscosity; binary mixtures; diffuse interfaces; Cahn–Hilliard equations; global attractors; exponential attractors; fractal dimension

Maurizio Grasselli  1   ; Dalibor Pražák  2

1 Politecnico di Milano, Italy
2 Charles University, Prague, Czech Republic 
Maurizio Grasselli; Dalibor Pražák. Longtime behavior of a diffuse interface model for binary fluid mixtures with shear dependent viscosity. Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 507-530. doi: 10.4171/ifb/270
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     title = {Longtime behavior of a diffuse interface model for binary fluid mixtures with shear dependent viscosity},
     journal = {Interfaces and free boundaries},
     pages = {507--530},
     year = {2011},
     volume = {13},
     number = {4},
     doi = {10.4171/ifb/270},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/270/}
}
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