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

• Published in: Journal of applied mechanics and technical physics Vol. 59; no. 5; pp. 928 - 933
• Main Author: Knyazev, D. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-09-2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Classical and Continuum Physics; Classical Mechanics; Dependence; Equations of motion; Fluid dynamics; Fluid- and Aerodynamics; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mechanical Engineering; Physics; Physics and Astronomy; Series (mathematics); Three dimensional motion; Viscous fluids; Navier–Stokes equations; exact solutions; separation of variables; overdetermined system
• ISSN: 0021-8944; 1573-8620
• DOI: 10.1134/S0021894418050218

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.