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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 
@article{VTPMK_2022_1_a0,
     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},
     pages = {5--17},
     year = {2022},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a0/}
}
TY  - JOUR
AU  - V. V. Grigoryeva
AU  - Yu. V. Sheretov
TI  - On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2022
SP  - 5
EP  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a0/
LA  - ru
ID  - VTPMK_2022_1_a0
ER  - 
%0 Journal Article
%A V. V. Grigoryeva
%A Yu. V. Sheretov
%T On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2022
%P 5-17
%N 1
%U http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a0/
%G ru
%F VTPMK_2022_1_a0
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/

[1] Lojtsyanskij L. G., Fluid and Gas Mechanics, Nauka Publ., Moscow, 1987, 840 pp. (in Russian)

[2] Landau L. D., Lifshits E. M., Hydrodynamics, Nauka Publ., Moscow, 1986, 736 pp. (in Russian) | MR

[3] Riley N., Drazin P. G., The Navier–Stokes equations: A classification of flows and exact solutions, Cambridge University Press, Cambridge, 2006, 196 pp. | MR | Zbl

[4] Shmyglevskij Yu. D., Analytical Investigations of Gas and Fluid Dynamics, Editorial URSS Publ., Moscow, 1999, 232 pp. (in Russian)

[5] Pukhnachev V. V., “Symmetries in the Navier-Stokes equations”, Achievements in Mechanics, 2006, no. 1, 6–76 (in Russian)

[6] Wang C. Y., “Exact solutions of the unsteady Navier–Stokes equations”, Applied Mechanics Reviews, 42:11, Part 2 (1989), S269–S282 | DOI | MR | Zbl

[7] Sheretov Yu. V., “On uniqueness of the solutions for one dissipative system of hydrodynamic type”, Mathematical Modeling, 6:10 (1994), 35–45 (in Russian) | MR | Zbl

[8] Sheretov Yu. V., Continuum Dynamics under Spatiotemporal Averaging, Regular and Chaotic Dynamics Publ., Moscow, Izhevsk, 2009, 400 pp. (in Russian)

[9] Sheretov Yu. V., Regularized Hydrodynamic Equations, Tver State University, Tver, 2016, 222 pp. (in Russian)

[10] Sheretov Yu. V., “On common exact solutions of Navier-Stokes and quasi–hydrodynamic systems for nonstationary flows”, Herald of Tver State University. Series: Applied Mathematics, 2017, no. 3, 13–25 (in Russian) | DOI

[11] Sheretov Yu. V., “On the solutions of Cauchy problem for quasi-hydrodynamic system”, Herald of Tver State University. Series: Applied Mathematics, 2020, no. 1, 84–96 (in Russian) | DOI

[12] Sheretov Yu. V., “On classes of exact solutions of quasi-hydrodynamic system”, Herald of Tver State University. Series: Applied Mathematics, 2020, no. 2, 5–17 (in Russian) | DOI

[13] Sheretov Yu. V., “On the construction of exact solutions of two-dimensional quasi-hydrodynamic system”, Herald of Tver State University. Series: Applied Mathematics, 2021, no. 1, 5–20 (in Russian) | DOI

[14] Grigoreva V. V., Sheretov Yu. V., “On exact solutions of quasi-hydrodynamic system that don't satisfy the Navier-Stokes and Euler systems”, Herald of Tver State University. Series: Applied Mathematics, 2 (2021), 5–15 (in Russian) | DOI

[15] Kovalev V. P., Prosviryakov E. Yu., “A new class of non-helical exact solutions of the Navier-Stokes equations”, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 24:4 (2020), 762–768 | DOI | Zbl

[16] Stenina T. V., Elizarova T. G., Kraposhin M. V., “Regularized equations for disk pump simulation problems in OpenFOAM implementation”, Keldysh Institute preprints, 2020, 066, 30 pp. (in Russian) | DOI

[17] Balashov V. A., Zlotnik A. A., “An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations”, Journal of Computational Dynamics, 7:2 (2020), 291–312 | DOI | MR | Zbl

[18] Balashov V. A., “Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow”, Computers and Mathematics with Applications, 90:112 (2021), 124 | DOI | MR | Zbl

[19] Zlotnik A. A., Fedchenko A. S., Properties of an aggregated quasi-hydrodynamic system of equations of a homogeneous gas mixture with a common regularizing velocity, 2021, 26 pp. (in Russian) | DOI

[20] Kraposhin M. V., Ryazanov D. A.Elizarova.T. G., “Numerical algorithm based on regularized equations for incompressible flow modeling and its implementation in OpenFOAM”, Computer Physics Communications, 271:1 (2022), 108216 | DOI | MR