Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
复制标题
DOI：
10.1007/s00526-022-02271-y
复制
发表时间：
2021-08
影响因子：
2.1
通讯作者：
H. Garcke;P. Knopf;Sourav Mitra;A. Schlömerkemper
中科院分区：
文献类型：
--
作者：
H. Garcke;P. Knopf;Sourav Mitra;A. Schlömerkemper
本文研究了二维不可压缩磁粘弹流体模型的强适定性、稳定性和最优控制问题。该模型包括一个不可压缩的Navier-Stokes方程的速度场，变形张量的演化方程，和一个梯度流方程的磁化矢量。首先，我们证明了所考虑的模型在适当的函数框架下具有全局强解。其次，我们得到稳定性估计相对于外部磁场。基于稳定性估计，我们使用外部磁场作为控制，以最小化跟踪型的成本泛函。我们证明了最优控制的存在性，并推导出一阶必要的最优性条件。最后，我们考虑第二个最优控制问题，其中外部磁场，这代表了控制，是由有限数量的固定磁场线圈产生的。
In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an incompressible Navier–Stokes equation for the velocity field, an evolution equation for the deformation tensor, and a gradient flow equation for the magnetization vector. First, we prove that the model under consideration posseses a global strong solution in a suitable functional framework. Second, we derive stability estimates with respect to an external magnetic field. Based on the stability estimates we use the external magnetic field as the control to minimize a cost functional of tracking-type. We prove existence of an optimal control and derive first-order necessary optimality conditions. Finally, we consider a second optimal control problem, where the external magnetic field, which represents the control, is generated by a finite number of fixed magnetic field coils.