A priori estimates on the semiaxis t≥0 for the solutions of the equations of motion of linear viscoelastic fluids with an infinite Dirichlet integral, and their applications

Abstract

The solvability on the semiaxis t≥0 of initial-boundary value problems are investigated for the equations of the motion of linear viscoelastic fluids — Oldroyd fluids and Kelvin—Voight fluids—for which the right-hand sides satisfy the conditions f, ft ∈ L∞(R+; L2(Ω)). The existence of “small” stable solutions, periodic with respect to t, is proved for the equations of the motion of Oldroyd fluids and Kelvin—Voight fluids, with a “small” right-hand side f, periodic with respect to t.