Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory

This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of incompressible viscoelastic fluid Jeffreys–Oldroyd type within fixed bounded region subject to no-slip boundary condition. Control parameters are included in initial The objective control is match velocity field at final time prescribed target field. model under consideration interpreted as continuous evolution infinite-dimensional Hilbert space. existence least one optimal proved inclusion-type constraints admissible controls.