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Convergence to equilibrium for a phase-field model for the mixture of two viscous incompressible fluids. (English) Zbl 1183.35224
Summary: We study the existence and long-time behavior of global strong solutions to a system describing the mixture of two viscous incompressible Newtonian fluids of the same density. The system consists of a coupling of Navier-Stokes and Cahn-Hilliard equations. We first show the global existence of strong solutions in several cases. Then we prove that the global strong solution of our system converges to a steady state as time goes to infinity. We also provide an estimate on the convergence rate.

MSC:
35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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