Pontryagin's principle and variational inequality for optimal control problems governed by viscous Camassa–Holm equations.

In this paper we prove the existence of optimal solutions as well as first-order necessary optimality conditions for a distributed optimal control problem governed by the three-dimensional viscous Camassa–Holm equations in bounded domains with the cost function of a quite general form. Particularly, in the box constraints case, the connection between the first-order necessary optimality conditions in the variational inequality form and the Pontryagin minimum principle is also established. [ABSTRACT FROM AUTHOR]