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.

Ключевые слова: газовая динамика, квазигазодинамическая система уравнений, уравнение баланса энтропии, регуляризация, the entropy balance equation, gas dynamics, regularization, уравнения Навье-Стокса сжимаемого газа, quasi-gasdynamic system of equations, compressible Navier-Stokes system of equations, smallness of perturbations, малость возмущений