论文标题
二维三年级流体的最佳控制
Optimal control of two dimensional third grade fluids
论文作者
论文摘要
这项工作的目的是研究由具有Navier-Slip边界条件的不可压缩的三年级流体方程所控制的流量的最佳控制问题。在回顾了状态方程良好的结果之后，我们研究了对线性化状态和伴随方程的解决方案的存在和唯一性。此外，我们给出了状态的稳定性结果，并表明线性化方程的解与控制对状态映射的Gâteaux导数相吻合。接下来，我们证明存在最佳解决方案并建立一阶最佳条件。最后，在足够大的成本强度下，建立了由状态方程，伴随方程和一阶最优条件构成的耦合系统的唯一性结果。
The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations, we study the existence and the uniqueness of solution to the linearized state and adjoint equations. Furthermore, we present a stability result for the state, and show that the solution of the linearized equation coincides with the Gâteaux derivative of the control-to-state mapping. Next, we prove the existence of an optimal solution and establish the first order optimality conditions. Finally, an uniqueness result of the coupled system constituted by the state equation, the adjoint equation and the first order optimality condition is established, under sufficiently large intensity of the cost.
