Geodesic
Exact solutions to generalized plane Beltrami–Trkal and~Ballabh flows
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 2, pp. 319-330

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Nonstationary plane flows of a viscous incompressible fluid in a potential field of external forces are considered. An elliptic partial differential equation is obtained, with each solution being a vortex flow stream function described by an exact solution to the Navier–Stokes equations. The obtained solutions generalize the Beltrami–Trkal and Ballabh flows. Examples of such new solutions are given. They are intended to verify numerical algorithms and computer programs.
Keywords: exact solutions to the Navier–Stokes equations, Beltrami–Trkal flow, Ballabh flow. 
@article{VSGTU_2020_24_2_a4,
     author = {E. Yu. Prosviryakov},
     title = {Exact solutions to generalized plane {Beltrami{\textendash}Trkal} {and~Ballabh} flows},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {319--330},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_2_a4/}
}
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E. Yu. Prosviryakov. Exact solutions to generalized plane Beltrami–Trkal and~Ballabh flows. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 2, pp. 319-330. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_2_a4/