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Symmetry reduction and exact solutions of the Navier-Stokes equations

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arxiv math-ph/0207016 v2 pith:7R6MRAYL submitted 2002-07-11 math-ph math.MPnlin.SIphysics.flu-dyn

Wilhelm I. Fushchych , Roman O. Popovych This is my paper · ORCID
classification math-phmath.MPnlin.SIphysics.flu-dyn
keywords equationsnavier-stokesansatzesexactsolutionsconstructeddescribeddifferential
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Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.

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  1. Extended symmetry analysis of two-dimensional degenerate Burgers equation

    math.AP 2019-08 accept novelty 7.0 of 10

    For the degenerate Burgers equation u_t + u u_x - u_yy = 0, all generalized symmetries reduce to Lie symmetries, and conservation laws are in one-to-one correspondence with solutions of the backward heat equation.

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