Opuscula Mathematica
Opuscula Math. 42, no. 5 (2022), 709-725

On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations

Muvasharkhan Jenaliyev
Murat Ramazanov
Madi Yergaliyev
Abstract. The paper studies the numerical solution of the inverse problem for a linearized two-dimensional system of Navier-Stokes equations in a circular cylinder with a final overdetermination condition. For a biharmonic operator in a circle, a generalized spectral problem has been posed. For the latter, a system of eigenfunctions and eigenvalues is constructed, which is used in the work for the numerical solution of the inverse problem in a circular cylinder with specific numerical data. Graphs illustrating the results of calculations are presented.
Keywords: Navier-Stokes equations, inverse problem, numerical solution.
Mathematics Subject Classification: 35Q30, 35R30, 65N21.
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About the authors ▼
Muvasharkhan Jenaliyev
https://orcid.org/0000-0001-8743-7026
Institute of Mathematics and Mathematical Modeling, Department of Differential Equations, Pushkin Str. 125, 050010 Almaty, Republic of Kazakhstan
Murat Ramazanov
https://orcid.org/0000-0002-2297-5488
Institute of Mathematics and Mathematical Modeling, Department of Differential Equations, Pushkin Str. 125, 050010 Almaty, Republic of Kazakhstan; E.A. Buketov Karaganda University, Department of Differential Equations, University Str. 28, 100028 Karaganda, Republic of Kazakhstan
Madi Yergaliyev (corresponding author)
https://orcid.org/0000-0001-8638-4647
Institute of Mathematics and Mathematical Modeling, Department of Differential Equations, Pushkin Str. 125, 050010 Almaty, Republic of Kazakhstan; Al-Farabi Kazakh National University, Department of Mechanics and Mathematics, 71 Al-Farabi Ave., 050040 Almaty, Republic of Kazakhstan
About the article ▼
Communicated by Mirosław Lachowicz.
Received: 2022-03-14.
Revised: 2022-07-19.
Accepted: 2022-07-24.
Published online: 2022-09-08.
Cite this article as ▼
Muvasharkhan Jenaliyev, Murat Ramazanov, Madi Yergaliyev, On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations, Opuscula Math. 42, no. 5 (2022), 709-725, https://doi.org/10.7494/OpMath.2022.42.5.709.
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