Abstract
In this paper, we study an optimal control problem of the three-dimensional viscous Camassa–Holm equations in bounded domains with Dirichlet boundary conditions and a quadratic objective functional. We first prove the existence of an optimal solution. Then we establish the first-order necessary and second-order sufficient optimality conditions.
Acknowledgments
The authors would like to thank the reviewers for their helpful comments and suggestions, which improved the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.