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Article information
2025 , Volume 30, ¹ 4, p.66-76
Bautin S.P., Vazieva I.A., Obukhov A.G.
Representation of two-dimensional solutions for the complete system of Navier-Stokes equations using trigonometric series
The paper addresses the complete set of Navier–Stokes equations in the case of two independent spatial variables. Solutions of these equations describe the flows of compressible viscous heat conducting gas. The Cauchy problem with continuous initial data is posed in the squared on the xOy plane. Ñontinuation of these data on the second square leads to the solution of the Cauchy problem which is presented in the form of corresponding trigonometric series for spatial variables. The coefficients of the series are the desired functions of time. Infinite system of ordinary differential equations with corresponding initial conditions for these coefficients is presented. Finite segments of trigonometric sums approximating the solutions of the Cauchy problem under consideration are presented.
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Keywords: the complete system of Navier-Stokes equations, the Cauchy problem, trigonometric series, approximate solutions
Author(s):
Bautin Sergey Petrovich
Dr. , Associate Professor
Position: Professor
Office: Snezhinsk Institute of Physics and Technology National Research Nuclear University MEPhI
Address: 456776, Russia, Snezhinsk, Komsomol str., 8
Phone Office: (343) 221 25 49
E-mail: SPBautin@mail.ru
SPIN-code: 4343-3821Vazieva Irina Alexandrovna
Position: Senior Fellow
Office: Snezhinsky Institute of Physics and Technology, National Research Nuclear University MEPhI
Address: 456776, Russia, Snezhinsk, 8 Komsomolskaya St.
Obukhov Alexander Gennadievich
Dr. , Professor
Office: Tyumen Industrial University
Address: 625000, Russia, Tyumen, 38 Volodarsky St.
Bibliography link:
Bautin S.P., Vazieva I.A., Obukhov A.G. Representation of two-dimensional solutions for the complete system of Navier-Stokes equations using trigonometric series // Computational technologies. 2025. V. 30. ¹ 4. P. 66-76
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