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We consider the statement of an initial boundary value problem for ageneralized Oldroyd model describing both laminar and turbulent flows of anonlinear visco-elastic fluid. The operator interpretation of a posedproblem is presented. The properties of operators forming the correspondingequation are investigated. We introduce approximating operator equationsand prove their solvability. On that base the existence theorem for theoperator equation equivalent to the stated initial boundary value problemis proved.

On weak solutions for some model of motion of nonlinear viscous-elastic fluid