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Global existence of weak solutions to a diffuse interface model for magnetic fluids |
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| Affiliation: | 1. Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria;2. Institut für Mathematik, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria;1. Department of Mathematics, University of Houston, Houston, TX 77204, United States;2. Sechenov University, Moscow, Russian Federation;1. Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi 9, 20133 Milano, Italy;2. Indiana University, Department of Mathematics, Rawles Hall, Bloomington, IN 47405, USA |
| Abstract: | This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier–Stokes equations coupled with an evolutionary equation for the magnetization vector and the Cahn–Hilliard equations. We show global in time existence of weak solutions to the system using the time discretization method. |
| Keywords: | Cahn–Hilliard equations Diffuse interface model Global existence Magnetization Incompressible Navier–Stokes equations Weak solution |
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