Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids (Q2153943)

In this paper, the authors study 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. By applying various tools and methods, e.g., Galerkin scheme, interpolation inequalities, energy method, and variational method, etc., the authors prove the strong well-posedness, stability and optimal control for the considered problem. In particular, it is the first time to study optimal control of the magneto-viscoelastic fluid model in the literature.