Solving The Motion Equations of a Viscous Fluid with a Nonlinear Dependence Between a Velocity Vector and some Spatial Variables

Abstract

It is shown that the classes of exact solutions of Navier–Stokes equations with a linear and inversely proportional dependence between velocity components and some spatial variables can be expanded by adding finite perturbations, being power and trigonometric series or their sections on one of the coordinates. An example of single integration of the three-dimensional motion equations a viscous fluid, reduced to an equation for the potential of two velocity components, is given.