Optimal Boundary Control of the Incompressible Fluid Problems in Rotation form

Problem Statement: We consider the optimal boundary control of the linearized Navier-Stokes problem. Both the Stokes problem and Oseen problem in rotation form are considered. Approach: We use the Mark and Cell (MAC) discretization method to discretize the optimization problem with linear constraints including the Stokes problem and the Oseen problem in rotation from. Then Reduced Hessian methods are to solve the problem. Results: Numerical experimental results are performed for the boundary optimization problem with the Stokes constraints and Oseen constraints. All the computed solutions and the desired solutions are compared. Conclusions: The proposed reduced Hessian methods have a high accuracy obtaining the optimal boundary conditioning for the Stokes problem and the Oseen problem in rotation form.