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## The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures

 1 Department of Mathematics & The Institute for Scientific Computing, and Applied Mathematics, Indiana University, Bloomington, Indiana 47405, USA 2 Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607, USA

* Corresponding author: Andrea Giorgini

Received  January 2020 Published  April 2020

We study the well-posedness for the mildly compressible Navier-Stokes-Cahn-Hilliard system with non-constant viscosity and Landau potential in two and three dimensional domains.

Citation: Andrea Giorgini, Roger Temam, Xuan-Truong Vu. The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020141
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