caa a22 4500 44584986X CHVBK 20180317145410.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1134/S0040579511060091 doi (NATIONALLICENCE)springer-10.1134/S0040579511060091 A new method for constructing exact solutions to three-dimensional Navier-Stokes and Euler equations [Elektronische Daten] [A. Polyanin, S. Aristov] Formulas are derived that make it possible to construct new exact solutions for three-dimensional stationary and nonstationary Navier-Stokes and Euler equations using simpler solutions to the respective two-dimensional equations. The formulas contain from two to five additional free parameters, which are not present in the initial solutions to the two-dimensional equations. It is important that these formulas do not contain quadratures in the steady-state case. We consider some examples of constructing new three-dimensional exact solutions to the Navier-Stokes equations using the derived formulas. The results are used to solve some problems of the hydrodynamics of a viscous incompressible liquid. Examples of thenonuniqueness of solutions to steady-state problems are given. Some three-dimensional solutions to the Navier-Stokes equations are constructed using nonviscous solutions to the Euler equations. Two classes of new exact solutions to the Grad-Shafranov equation that contain functional arbitrariness are specified. Note that, in this study, a new method for constructing exact solutions is applied that can be useful for analyzing other nonlinear physical models and phenomena. Several physical and physicochemical systems where this method can be used are considered. Pleiades Publishing, Ltd., 2011 Polyanin A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, 119526, Moscow, Russia aut Aristov S. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, 614013, Perm, Russia aut Theoretical Foundations of Chemical Engineering SP MAIK Nauka/Interperiodica 45/6(2011-12-01), 885-890 0040-5795 45:6<885 2011 45 11236 https://doi.org/10.1134/S0040579511060091 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0040579511060091 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Polyanin A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, 119526, Moscow, Russia aut NATIONALLICENCE 700 1- Aristov S. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, 614013, Perm, Russia aut NATIONALLICENCE 773 0- Theoretical Foundations of Chemical Engineering SP MAIK Nauka/Interperiodica 45/6(2011-12-01), 885-890 0040-5795 45:6<885 2011 45 11236 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer