In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly α-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.

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We investigate in this article Pontryagin's maximum principle for a class of control problems associated with a 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. We derive 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.

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