NUMERICAL SOLUTION OF A LINEAR SYSTEM OF NAVIER -- STOKES EQUATIONS IN AN AXISYMMETRIC DOMAIN

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.