Abstract
A new exact method of solving general threedi mensional nonstationary linearized equations for viscoelastic fluids is described based on breaking these equations down into several simpler equations. For� mulas are given that make it possible to express the solution in the respective systems (consisting of four con� nected equations) by solving two independent equations. The most widespread rheological models of vis� coelastic fluids are considered to illustrate the powerful capabilities of the proposed method. A new differen� tialdifference model for a viscous fluid with a const ant 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.
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