A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This aims to reconstruct velocity and kernel memory term simultaneously, measurement described as integral over determination condition. By using contraction mapping principle appropriate space, a local time existence uniqueness result are obtained. Furthermore, similar arguments, global results Oseen equations also achieved.