On steady motion of viscoelastic fluid of Oldroyd type
The author considers steady flow of a viscoelastic fluid of Oldroyd type with the regularized Jaumann derivative. Assuming the slip boundary conditions on the fixed walls, the author proves the existence of a solution to the corresponding system of partial differential equations. Additionally, he shows that the set of solutions is sequentially weakly closed. The proof is based on the fact that it is possible to obtain a priori estimates for the velocity and the elastic component of the shear stress.NEWLINENEWLINENext, he studies the flow of this fluid in an infinite channel with flat walls under slip boundary conditions and constructs analytically the solution to this problem.
scientific article; zbMATH DE number 6349850