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A Particular Class of Partially Invariant Solutions of the Navier—Stokes Equations

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Abstract

One class of partially invariant solutions of the Navier—Stokes equations is studied here. This class of solutions is constructed on the basis of the four-dimensional algebra L 4 with the generators \(\begin{array}{*{20}c} {X_1 = \phi _1 \partial _x + \phi '_1 \partial _u - x\phi ''_1 \partial _p ,\quad X_2 = \phi _2 \partial _x + \phi '_2 \partial _u - x\phi ''_2 \partial _p ,} \\ {Y_1 = \psi _1 \partial _y + \psi '_1 \partial _v - y\psi ''_1 \partial _p ,\quad Y_2 = \psi _2 \partial _y + \psi '_2 \partial _v - y\psi ''_2 \partial _p .} \\ \end{array}\)

Systematic investigation of the case, where the Monge—Ampere equation (10) is hyperbolic (Lf z + k + l ≥ 0) is given. It is shown that this class of solutions is a particular case of the solutions with linear velocity profile with respect to one or two space variables.

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  1. School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    Sergey V. Meleshko

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  1. Sergey V. Meleshko
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Meleshko, S.V. A Particular Class of Partially Invariant Solutions of the Navier—Stokes Equations. Nonlinear Dynamics 36, 47–68 (2004). https://doi.org/10.1023/B:NODY.0000034646.18621.73

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