Geodesic
On the construction of exact solutions of two-dimensional quasi-hydrodynamic system
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2021), pp. 5-20

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New methods for constructing exact solutions of the quasi-hydrodynamic system for two-dimensional flows are proposed. It is shown that with any smooth solution of some overdetermined system of partial differential equations one can associate common exact solution of the quasi-hydrodynamic system and the Navier-Stokes system. Any eigenfunction of the two-dimensional Laplace operator also generates common solution to these systems. Examples of solutions are given in both the non-stationary and stationary cases. The principle of superposition of the fluid velocity vector fields for specific flows is discussed.
Keywords: Navier-Stokes system, principle of superposition.
Mots-clés : quasi-hydrodynamic system, exact solutions 
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Yu. V. Sheretov. On the construction of exact solutions of two-dimensional quasi-hydrodynamic system. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2021), pp. 5-20. http://geodesic.mathdoc.fr/item/VTPMK_2021_1_a0/