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

T. Tachim Medjo

doi:10.3934/cpaa.2016028

Article Contents

2016, Volume 15, Issue 6: 2075-2101. Doi: 10.3934/cpaa.2016028

This issue Previous Article On the Hardy-Littlewood-Sobolev type systems Next Article Boundedness and stability of solutions to semi-linear equations and applications to fluid dynamics

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

T. Tachim Medjo^1,

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

Received: October 31, 2015

Revised: February 29, 2016

Published: October 2016

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Abstract

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.

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Mathematics Subject Classification: 93C05, 93B50, 93C35.

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