On the dissipative properties of quasi–hydrodynamic equations in Stokes approximation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2016), pp. 95-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For non-stationary quasi-hydrodynamic equations in Stokes approximation new proof of the theorem on the dissipation of total kinetic energy $E(t)$ is proposed. It is shown, that $E(t)$ not only decreases and tends to zero under $t\to +\infty$, but it is convex down function.
Mots-clés : quasi-hydrodynamic equations
Keywords: Stokes approximation, dissipative properties.
@article{VTPMK_2016_2_a5,
     author = {V. V. Grigoryeva and Yu. V. Sheretov},
     title = {On the dissipative properties of quasi{\textendash}hydrodynamic equations in {Stokes} approximation},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {95--105},
     year = {2016},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a5/}
}
TY  - JOUR
AU  - V. V. Grigoryeva
AU  - Yu. V. Sheretov
TI  - On the dissipative properties of quasi–hydrodynamic equations in Stokes approximation
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2016
SP  - 95
EP  - 105
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a5/
LA  - ru
ID  - VTPMK_2016_2_a5
ER  - 
%0 Journal Article
%A V. V. Grigoryeva
%A Yu. V. Sheretov
%T On the dissipative properties of quasi–hydrodynamic equations in Stokes approximation
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2016
%P 95-105
%N 2
%U http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a5/
%G ru
%F VTPMK_2016_2_a5
V. V. Grigoryeva; Yu. V. Sheretov. On the dissipative properties of quasi–hydrodynamic equations in Stokes approximation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2016), pp. 95-105. http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a5/

[1] Ladyzhenskaya O. A., Mathematical Theory of Viscous Incompressible Fluid, Nauka Publ., Moscow, 1970, 288 pp. (in Russian)

[2] 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

[3] Sheretov Yu. V., Mathematical Modeling of Fluid and Gas Flows on the Basis of Quasi-Hydrodynamic Equations, Tver State University, Tver, 2000, 235 pp. (in Russian)

[4] Sheretov Yu. V., Dynamics of Continuous Media with Spatial-Temporal Averaging, NITS “Regular and Chaotic Dynamics”, Moscow, Izhevsk, 2009, 400 pp. (in Russian)

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

[6] Zherikov A. V., Application of Quasi-Hydrodynamic Equations: Mathematical Modeling of Viscous Incompressible Fluid, Lambert Academic Publishing, Saarbrücken, 2010, 124 pp. (in Russian)

[7] Sheretov Yu. V., “Methods for constructing exact solutions of quasi-hydrodynamic equations”, Vestnik TvGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2011, no. 21, 5–26 (in Russian)

[8] Grigoryeva V. V., Sheretov Yu. V., “Solution of the Cauchy problem for quasi-hydrodynamic equations in the Stokes approximation”, Application of Functional Analysis in Approximation Theory, Tver State University, Tver, 2015, 50–55 (in Russian)

[9] Rektoris K., Variational Methods in Mathematical Physics and Engineering, Mir Publ., Moscow, 1985, 589 pp. (in Russian) | MR