Geodesic
On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2022), pp. 5-17

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The quasi-hydrodynamic system was proposed by Sheretov Yu.V. in 1993. It differs from the Navier-Stokes system in dynamics of a viscous incompressible fluid by the additional divergent terms. In this paper, the Gromeki-Beltrami method is used to construct a new one-parameter family of exact solutions of a quasi-hydrodynamic system, which also satisfy to the Navier-Stokes system. This family is generated by the eigenfunction of two-dimensional Laplace operator.
Keywords: Navier-Stokes system, Gromeka-Beltrami method, eigenfunction of two-dimensional Laplace operator.
Mots-clés : quasi-hydrodynamic system, exact solutions 
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     author = {V. V. Grigoryeva and Yu. V. Sheretov},
     title = {On a new class of exact solutions of {Quasi-Hydrodynamic} system, generated by eigenfunctions of two-dimensional {Laplace} operator},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
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     publisher = {mathdoc},
     number = {1},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a0/}
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V. V. Grigoryeva; Yu. V. Sheretov. On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2022), pp. 5-17. http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a0/