Initial boundary value problems for linear viscoelastic flows generated by integrodifferential equations

An estimate of the velocity field is obtained for the equation of motion of incompressible media. With the help of this estimate, the integro-differential equations that describe the motion of linear viscoelastic fluids in the twodimensional case are studied. The existence is proved for a weak, global in time, solution of the Cauchy problem and of the initial boundary value problem with periodic boundary conditions.