V. V. Grigoryeva, Yu. V. Sheretov, “On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2022, Issue 1,Pages <nobr>5

This article is cited in 1 paper

Mathematical Modelling, Numerical Methods and Software Systems

On a new class of exact solutions of Quasi-Hydrodynamic system, generated by eigenfunctions of two-dimensional Laplace operator

V. V. Grigoryeva^a, Yu. V. Sheretov^b

^a Tver State Technical University, Tver
^b Tver State University, Tver

Abstract: The quasi-hydrodynamic system was proposed by Sheretov Yu.V. in 1993. It differs from the Navier-Stokes system in dynamics of a viscous incompressible fluid by the additional divergent terms. In this paper, the Gromeki-Beltrami method is used to construct a new one-parameter family of exact solutions of a quasi-hydrodynamic system, which also satisfy to the Navier-Stokes system. This family is generated by the eigenfunction of two-dimensional Laplace operator.

Keywords: Navier-Stokes system, quasi-hydrodynamic system, Gromeka-Beltrami method, exact solutions, eigenfunction of two-dimensional Laplace operator.

UDC: 517.95, 532.5

Received: 10.01.2022
Revised: 20.01.2022

DOI: 10.26456/vtpmk631