Abstract:
The paper presents a new class of exact solutions for the Navier–Stokes
equations. These solutions describe unsteady three-dimensional in velocities
and two-dimensional in coordinates for a viscous incompressible fluid flow.
The procedure for constructing an exact solution generalizes Trkal's method
proposed for studying screw flows. The new class of exact solutions allows
to describe non-hecical flows (the velocity vector forms a nonzero angle
with the vorticity vector) and fluid flows existing in a finite time.
Keywords:
Navier-Stokes equation, exact solution, Trkal's method, eigenfunctions of the Laplacian, non-helical flows, blow-up regimes.
Citation:
V. P. Kovalev, E. Yu. Prosviryakov, “A new class of non-helical exact solutions of the Navier–Stokes equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:4 (2020), 762–768
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\by V.~P.~Kovalev, E.~Yu.~Prosviryakov
\paper A new class of non-helical exact solutions of~the~Navier--Stokes equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 4
\pages 762--768
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\crossref{https://doi.org/10.14498/vsgtu1814}
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Linking options:
https://www.mathnet.ru/eng/vsgtu1814
https://www.mathnet.ru/eng/vsgtu/v224/i4/p762
This publication is cited in the following 5 articles:
E. Yu. Prosviryakov, O. A. Ledyankina, L. S. Goruleva, “Exact Solutions to the Navier–Stokes Equations for Describing the Flow of Multicomponent Fluids with Internal Heat Generation”, Russ. Aeronaut., 67:1 (2024), 60
E. Yu. Prosviryakov, O. A. Ledyankina, L. S. Goruleva, “A Class of Exact Solutions of Magnetic Hydrodynamics Equations for Describing Convective Flows of Multilayer Fluids”, Russ. Aeronaut., 67:3 (2024), 550
L. S. Goruleva, E. Yu. Prosviryakov, “A New Class of Exact Solutions to Magnetohydrodynamics Equations for Describing Convective Flows of Binary Fluids”, Tech. Phys., 68:10 (2023), 292
Subin P. Joseph, “Families of superposable planar exact solutions for skew-symmetric couple stress fluid flows”, Acta Mech, 234:7 (2023), 2819
Larisa Goruleva, Evgenii Prosviryakov, “A New Class of Exact Solutions for Magnetohydrodynamics Equations to Describe Convective Flows of Binary Liquids”, HFIM, 25:4 (2023)
Citation in format AMSBIB
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