Geodesic
Exact solutions of quasi-hydrodynamic system on the base of Biot-Savart formula
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 38-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The quasi-hydrodynamic system for a slightly compressible viscous fluid was proposed by the author in 1993. In the work new exact solutions of this system for steady-state flows are constructed. They also satisfy to Euler and Navier-Stokes systems. The velocity field is calculated as the sum of Biot-Savart integral and gradient of harmonic function. The substantiation of the approach is made, the corresponding theorems are proved. Physical interpretation of solutions is given. The meaning of included constants is clarified.
Mots-clés : quasi-hydrodynamic system, exact solutions, Biot-Savart formula.
Keywords: Euler and Navier-Stokes equations 
@article{VTPMK_2019_1_a3,
     author = {Yu. V. Sheretov},
     title = {Exact solutions of quasi-hydrodynamic system on the base of {Biot-Savart} formula},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {38--49},
     year = {2019},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a3/}
}
TY  - JOUR
AU  - Yu. V. Sheretov
TI  - Exact solutions of quasi-hydrodynamic system on the base of Biot-Savart formula
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2019
SP  - 38
EP  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a3/
LA  - ru
ID  - VTPMK_2019_1_a3
ER  - 
%0 Journal Article
%A Yu. V. Sheretov
%T Exact solutions of quasi-hydrodynamic system on the base of Biot-Savart formula
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2019
%P 38-49
%N 1
%U http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a3/
%G ru
%F VTPMK_2019_1_a3
Yu. V. Sheretov. Exact solutions of quasi-hydrodynamic system on the base of Biot-Savart formula. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2019), pp. 38-49. http://geodesic.mathdoc.fr/item/VTPMK_2019_1_a3/

[1] Sivukhin D. V., General course of physics, Nauka Publ., Moscow, 1983, 688 pp. (in Russian)

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

[3] 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

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

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

[6] Sheretov Yu. V., “On the common exact solutions of stationary Navier-Stokes and quasi–hydrodynamic systems, not satisfying to Euler equations”, Herald of Tver State University. Series: Applied Mathematics, 2017, no. 2, 5–15 (in Russian) | DOI

[7] 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

[8] Sheretov Yu. V., “On the exact solutions of quasi–hydrodynamic system that satisfy the generalized Gromeki-Beltrami condition”, Herald of Tver State University. Series: Applied Mathematics, 2018, no. 3, 5–18 (in Russian) | DOI

[9] Lavrentev M. A., Shabat B. V., Methods of the theory of functions of a complex variable, Nauka Publ., Moscow, 1987, 688 pp. (in Russian)