Geodesic
On common exact solutions of Navier-Stokes and quasi-hydrodynamic systems for nonstationary flows
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2017), pp. 13-25

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It is shown that the Trkal method for constructing uniformly-helical solutions of nonstationary Navier-Stokes equations is applicable for quasi-hydrodynamic system. A wider class of flows, obeying the generalized Gromeki-Beltrami condition, is considered. Examples of exact solutions, common to the Navier-Stokes and quasi-hydrodynamic systems, but not satisfying the Euler equations, are given.
Keywords: Navier-Stokes and Euler systems, Trkal method, generalized Gromeka-Beltrami condition, helical flows.
Mots-clés : quasi-hydrodynamic equations, exact solutions 
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     author = {Yu. V. Sheretov},
     title = {On common exact solutions of {Navier-Stokes} and quasi-hydrodynamic systems for nonstationary flows},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {13--25},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_3_a1/}
}
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Yu. V. Sheretov. On common exact solutions of Navier-Stokes and quasi-hydrodynamic systems for nonstationary flows. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2017), pp. 13-25. http://geodesic.mathdoc.fr/item/VTPMK_2017_3_a1/