Construction of solutions to the Cauchy problem for Quasi-hydrodynamic system using Lin's substitution

V. V. Grigoryeva ; Yu. V. Sheretov

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2024), pp. 5-16

Résumé

A new solution to the Cauchy problem for a nonstationary quasi-hydrodynamic system is constructed. It does not satisfy either the Navier-Stokes equations or the Euler equations. Using Lin's substitution, the quasi-hydrodynamic system was reduced to three partial differential equations. Three Cauchy problems were posed and solved for the indicated equations. These three solutions generate a new solution to the Cauchy problem for a quasi-hydrodynamic system. At $c_s\to +\infty$, where $c_s$ is the sound velocity in the fluid, it turns into the solution of the Cauchy problem for the corresponding Navier-Stokes system.

Détail

Mots-clés : quasi-hydrodynamic system, Lin's substitution.
Keywords: Navier-Stokes system, Cauchy problem

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