High-order iterative schemes for a system of nonlinear KirchhoffCarrier wave equations associated with the helical flows of Maxwellfluid

This paper is devoted to study of an initial-boundary value problem for the system of nonlinear Kirchhoff-Carrier wave equations associated with the helical flows of Maxwell fluid.Based on using the Faedo -Galerkin method together with constructing high order iterative schemes, the local existence and uniqueness of a weak solution are proved.Moreover, the sequence associated with high order iterative schemes here converges at a rate of high order to the unique weak solution.This result is an extension of the recent research, in which nonlinear wave equations associated with the helical flows of Maxwell fluid considered without the terms of Kirchhoff-Carrier type.