Geodesic
Construction of solutions to the Cauchy problem for Quasi-hydrodynamic system using Lin's substitution
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2024), pp. 5-16

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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.
Mots-clés : quasi-hydrodynamic system, Lin's substitution.
Keywords: Navier-Stokes system, Cauchy problem 
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     author = {V. V. Grigoryeva and Yu. V. Sheretov},
     title = {Construction of solutions to the {Cauchy} problem for {Quasi-hydrodynamic} system using {Lin's} substitution},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--16},
     publisher = {mathdoc},
     number = {4},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_4_a0/}
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V. V. Grigoryeva; Yu. V. Sheretov. Construction of solutions to the Cauchy problem for Quasi-hydrodynamic system using Lin's substitution. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2024), pp. 5-16. http://geodesic.mathdoc.fr/item/VTPMK_2024_4_a0/