# American Institute of Mathematical Sciences

November  2016, 15(6): 2075-2101. doi: 10.3934/cpaa.2016028

## Robust control of a Cahn-Hilliard-Navier-Stokes model

 1 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, United States

Received  November 2015 Revised  March 2016 Published  September 2016

We study in this article a class of robust control problems associated with a coupled Cahn-Hilliard-Navier-Stokes model in a two dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity, coupled with the Cahn-Hilliard model for the order (phase) parameter. We prove the existence and uniqueness of solutions and we derive a first-order necessary optimality condition for these robust control problems.
Citation: T. Tachim Medjo. Robust control of a Cahn-Hilliard-Navier-Stokes model. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2075-2101. doi: 10.3934/cpaa.2016028
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