Zhao, Liyun; Wu, Hao; Huang, Haiyang Convergence to equilibrium for a phase-field model for the mixture of two viscous incompressible fluids. (English) Zbl 1183.35224 Commun. Math. Sci. 7, No. 4, 939-962 (2009). 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. Cited in 32 Documents MSC: 35Q30 Navier-Stokes equations 35B40 Asymptotic behavior of solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:Navier-Stokes equation; Cahn-Hilliard equation; convergence to equilibrium; Lojasiewicz-Simon approach PDF BibTeX XML Cite \textit{L. Zhao} et al., Commun. Math. Sci. 7, No. 4, 939--962 (2009; Zbl 1183.35224) Full Text: DOI Euclid