This paper investigates the optimal control problem for the non-isentropic compressible Navier–Stokes equations linearized around a constant steady state. First, we establish estimates for the solution of the state equation. Then, we prove the existence and uniqueness of the optimal control, derive the necessary optimality conditions, and obtain an explicit characterization of the control via the optimality system. Finally, we present a numerical experiment to compute the control using the derived formula.
Pan et al. (Sat,) studied this question.