This article is cited in 1 paper

Mathematical Modelling, Numerical Methods and Software Systems

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

V. V. Grigoryeva^a, Yu. V. Sheretov<sup>b

a</sup> Tver State Technical University, Tver
^b Tver State University, Tver

Abstract: 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.

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

UDC: 517.95, 532.5

Received: 09.07.2024
Revised: 24.09.2024

DOI: 10.26456/vtpmk723

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