| Abstract: |
| We consider a diffuse interface model for an incompressible binary viscoelastic fluid flow. The model consists of the Navier-Stokes-Voigt equations where the instantaneous kinematic viscosity has been replaced by a memory term incorporating hereditary effects. These equations are coupled with the Cahn-Hilliard equation with Flory-Huggins type potential. The resulting system is subject to no-slip condition for the (volume averaged) fluid velocity and no-flux boundary conditions for the order parameter as well as for the chemical potential. The presence of a memory term entails hyperbolic features (i.e. the fluid velocity does not regularize in finite time). The corresponding initial and boundary value problem is well posed. Moreover, by adding an Eckman-type damping, we show that it defines a dissipative dynamical system in a suitable phase space, i.e., there is a bounded absorbing set. Then, we discuss the existence of global and exponential attractors. |
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