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Journal of Applied Mechanics and Technical Physics

2018 year, number 5

Solving the Motion Equations of a Viscous Liquid with a Nonlinear Dependence between a Velocity Vector and Some Spatial Variables

D. V. Knyazev
Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, 614013, Russia
Keywords: уравнения Навье - Стокса, точные решения, разделение переменных, переопределенные системы, Navier- Stokes equations, exact solutions, separation of variables, overdetermined system

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 or trigonometric series or their sections on one of the coordinates. An example of single integration of three-dimensional equations of motion of a viscous liquid, which are reduced to an equation for the potential of two velocity components, is given.