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

#### Abstract

We consider the statement of an initial boundary value problem for a

generalized Oldroyd model describing both laminar and turbulent flows of a

nonlinear visco-elastic fluid. The operator interpretation of a posed

problem is presented. The properties of operators forming the corresponding

equation are investigated. We introduce approximating operator equations

and prove their solvability. On that base the existence theorem for the

operator equation equivalent to the stated initial boundary value problem

is proved.

generalized Oldroyd model describing both laminar and turbulent flows of a

nonlinear visco-elastic fluid. The operator interpretation of a posed

problem is presented. The properties of operators forming the corresponding

equation are investigated. We introduce approximating operator equations

and prove their solvability. On that base the existence theorem for the

operator equation equivalent to the stated initial boundary value problem

is proved.

#### Keywords

Nonlinear viscous elastic fluids; laminar and turbulent flows; initial boundary value problem; operator equations; week solution; degree theory

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