Abstract

We investigate in this article the Pontryagin's maximum principle for a class of 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 v, coupled with a Cahn-Hilliard model for the order (phase) parameter φ. The optimal problems involve a state constraint similar to that considered by G. Wang [Optimal controls of 3-dimensional Navier-Stokes equations with state constraints, SIAM J. Control Optim. 41(2) (2002) 583–606]. We derive the Pontryagin's maximum principle for the control problems assuming that a solution exists. Let us note that the coupling between the Navier-Stokes and the Cahn-Hilliard systems makes the analysis of the control problem more involved.

Author information

Contact details are reproduced from the original publication and may be historical.

Theodore Tachim Medjo

Dept. of Mathematics, Florida International University, University Park, Miami, FL 33199, U.S.A.

tachimt@fiu.edu

Keywords

  • Two-phase flow model
  • maximum principle
  • state constraints

Mathematics Subject Classification

93C05,93B50,93C35

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Suggested citation

T. Tachim Medjo. “Optimal Control of a Cahn-Hilliard-Navier-Stokes Model with State Constraints.” Journal of Convex Analysis 22 (2015), No. 4, 1135–1172. https://doi.org/10.68381/jca22060

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press.