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.