Short Notes

Numerical solution of a linear system of Navier – Stokes equations in an axisymmetric domain

A. S. Konkina

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The system of Navier – Stokes equations simulates the dynamics of a viscous incompressible fluid. The problem on the existence of solutions to the Cauchy – Dirichlet problem for this system is one of the most difficult mathematical problems of the present century. However, the question on the existence of solutions to the Cauchy – Dirichlet problem for the system of Navier – Stokes equations still remains unsolved. This article shows how to obtain eigenvalues for the system in the case of an axisymmetric domain.

Keywords: system of Navier – Stokes equations, Galerkin method, multipoint initial-final value condition.

UDC: 517.9

MSC: 35G05

Received: 27.07.2019

Language: English

DOI: 10.14529/jcem190306