Geodesic
On exact solutions of quasi-hydrodynamic system that don't satisfy the Navier-Stokes and Euler systems
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 5-15

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The quasi-hydrodynamic system was proposed by Sheretov Yu.V. in 1993. The known exact solutions of this system in the overwhelming majority of cases satisfy either the Navier-Stokes equations or the Euler equations. This paper describes a new class of exact solutions of quasi-hydrodynamic system that satisfy neither the Navier-Stokes equations, nor the Euler equations. The corresponding exact solutions of the Navier-Stokes system are obtained from the constructed solutions by passing to the limit at $c_s\to +\infty$, where $c_s$ is the sonic velocity in the fluid.
Keywords: Navier-Stokes system, Euler system, principle of superposition.
Mots-clés : quasi-hydrodynamic system, exact solutions 
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     author = {V. V. Grigoryeva and Yu. V. Sheretov},
     title = {On exact solutions of quasi-hydrodynamic system that don't satisfy the {Navier-Stokes} and {Euler} systems},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--15},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a0/}
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V. V. Grigoryeva; Yu. V. Sheretov. On exact solutions of quasi-hydrodynamic system that don't satisfy the Navier-Stokes and Euler systems. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 5-15. http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a0/