Spatial local solutions of the Navier-Stokes equations |
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Authors: | R. M. Garipov |
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Affiliation: | (1) Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia |
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Abstract: | This paper considers solutions of the Navier-Stokes equations polynomial in the coordinates, which. are called local solutions. For an incompressible fluid, all higher-order terms (sums of higher-order. monomials) of degree 2 are found and it is proved that nontrivial axisymmetric higher-order terms. of degree higher than 2 do not exist. Nonsolenoidal axisymmetric solutions are listed, which can be. treated as steady-state barotropic gas flows in a potential external-force field. All elliptic vortices. generalizing the well-known Kirchhoff solution are calculated. All solutions of degree 3 with the. higher-order term of partial form are found. Some of these solutions break down in a finite time. regardless of the value and sign of viscosity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 109–119, March–April, 2009. |
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Keywords: | viscous fluid polynomial local solution higher-order term elliptic vortex |
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