Robust control problems in fluid mechanics

In this paper, we study a class of robust control problems in fluid mechanics recently proposed by Bewley et al. [Physica D 138 (3–4) (2000) 360]. Using a method of Shutyaev [Russ. J. Numer. Anal. Math. Modell. 14 (2) (1999) 137], we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to those of Bewley et al. [Physica D 138 (3–4) (2000) 360]. From the numerical point of view, the method used in this paper is particularly important since it provides a constructive way to approximate the solutions to these nonlinear control problems.