Geodesic
Numerical solution of a linear system of Navier -- Stokes equations in an axisymmetric domain
Journal of computational and engineering mathematics, Tome 6 (2019) no. 3, pp. 69-75.

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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. 
@article{JCEM_2019_6_3_a5,
     author = {A. S. Konkina},
     title = {Numerical solution of a linear system of {Navier} -- {Stokes} equations in an axisymmetric domain},
     journal = {Journal of computational and engineering mathematics},
     pages = {69--75},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_3_a5/}
}
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A. S. Konkina. Numerical solution of a linear system of Navier -- Stokes equations in an axisymmetric domain. Journal of computational and engineering mathematics, Tome 6 (2019) no. 3, pp. 69-75. http://geodesic.mathdoc.fr/item/JCEM_2019_6_3_a5/