Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects

Details Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects

2012-04-26

arxiv.org/abs/1204.6013v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Marangoni effects. The governing system consists of modified Navier--Stokes equations coupled with phase-field and energy transport equations. We first derive an energy inequality that illustrates the dissipative nature of the system under the assumption that the initial temperature variation is properly small. Then we establish the existence of weak/strong solutions via the energy method and discuss the long-time dynamics as well as stability of the system.

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