Decomposition of three-dimensional linearized equations for Maxwell and Oldroyd viscoelastic fluids and their generalizations

A new exact method of solving general three-dimensional nonstationary linearized equations for viscoelastic fluids is described based on breaking these equations down into several simpler equations. Formulas are given that make it possible to express the solution in the respective systems (consisting of four connected equations) by solving two independent equations. The most widespread rheological models of viscoelastic fluids are considered to illustrate the powerful capabilities of the proposed method. A new differential-difference model for a viscous fluid with a constant relaxation time is proposed that gives a finite disturbance propagation rate and is in good agreement with the Maxwell and Oldroyd differential models of viscoelastic fluids. The axial flows of viscoelastic fluids are studied, and solutions to certain hydrodynamic problems are given.