Exact Solutions for the Layered Three-Dimensional Nonstationary Isobaric Flows of Viscous Incompressible Fluid
N. M. Zubarev1,2, E. Yu. Prosviryakov3
1Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016, Russia
2Lebedev Physical Institute, Russian Academy of Science, Moscow, 119991, Russia
3Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016, Russia
Keywords: слоистые течения, изобарические течения, точные решения, переопределенная система уравнений, условия совместности, layered flows, isobaric flows, exact solutions, overdetermined system of equations, compatibility conditions
Abstract
This paper describes an overdetermined system of equations that describes three-dimensional layered unsteady flows of a viscous incompressible fluid at a constant pressure. Studying the compatibility of this system makes it possible to reduce it to coupled quasilinear parabolic equations for velocity components. The reduced equations allow constructing several classes of exact solutions. In particular, polynomial and spatially localized self-similar solutions of the motion equations are obtained. The passage to the limit of the case of an ideal fluid is investigated.
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