Abstract:
New methods for constructing exact solutions of the quasi-hydrodynamic system for two-dimensional flows are proposed. It is shown that with any smooth solution of some overdetermined system of partial differential equations one can associate common exact solution of the quasi-hydrodynamic system and the Navier-Stokes system. Any eigenfunction of the two-dimensional Laplace operator also generates common solution to these systems. Examples of solutions are given in both the non-stationary and stationary cases. The principle of superposition of the fluid velocity vector fields for specific flows is discussed.
Keywords:
Navier-Stokes system, quasi-hydrodynamic system, exact solutions, principle of superposition.
Received: 15.01.2021 Revised: 03.02.2021
Bibliographic databases:
Document Type:
Article
UDC:517.95, 532.5
Language: Russian
Citation:
Yu. V. Sheretov, “On the construction of exact solutions of two-dimensional quasi-hydrodynamic system”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2021, no. 1, 5–20
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\by Yu.~V.~Sheretov
\paper On the construction of exact solutions of two-dimensional quasi-hydrodynamic system
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2021
\issue 1
\pages 5--20
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\crossref{https://doi.org/10.26456/vtpmk605}
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Citation in format AMSBIB
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