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Статья

On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations

Russian Journal of Mathematical Physics. 2017. Vol. 24. No. 3. P. 299-309.
Chetverushkin B. N., Zlotnik A.A.

We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter $\tau>0$ and 2nd order space and time derivatives; the body force is taken into account. We transform it to the form close to the compressible Navier-Stokes system of equations. Then we derive the entropy balance equation and show that the entropy production is like for the latter system plus a term of the order $O(\tau^2)$. We analyze an equation for the total entropy as well. We also show that the corresponding residuals in the HQGD equations with respect to the compressible Navier-Stokes ones are of the order $O(\tau^2)$ too. Finally we treat the simplified barotropic HQGD system of equations with the general state equation and the stationary potential body force and obtain the corresponding results for it.