Abstract
Abstract This paper deals with the global unique solvability of two inverse problems for Kelvin–Voigt system with memory that governs the flow of incompressible non-Newtonian fluids with relaxation and elastic properties. Inverse problems that study here, consist of determining a time dependent intensity of the density of external forces, along with a velocity and a pressure of fluids. As additional information, two types of integral overdetermination conditions by space domain were taken. The system supplemented also with an initial and new sliding boundary condition, which has important physical meaning in the theory of motion of non-Newtonian fluids. For all considered inverse problems, under suitable assumptions on the data, the global in time existence and uniqueness of weak and strong solutions were established.