Optimal System of Subalgebras for the Reduction of the Navier-Stokes Equations

Abstract

The purpose of this paper is to find the admitted Lie group of the reduction of the Navier-Stokes equationswhere using the basic Lie symmetry method. This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Two-dimensional optimal system is determined for symmetry algebras obtained through classification of their subalgebras. Some invariant solutions are also found.

The purpose of this paper is to find the admitted Lie group of the reduction of the Navier-Stokes equationswhere using the basic Lie symmetry method. This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Two-dimensional optimal system is determined for symmetry algebras obtained through classification of their subalgebras. Some invariant solutions are also found.

Keywords

Optimal System; Invariant Solutions; Partially Invariant Solutions; Navier-Stokes Equations

Optimal System; Invariant Solutions; Partially Invariant Solutions; Navier-Stokes Equations

Cite this paper

S. Khamrod, "Optimal System of Subalgebras for the Reduction of the Navier-Stokes Equations,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 124-134. doi: 10.4236/am.2013.41022.

S. Khamrod, "Optimal System of Subalgebras for the Reduction of the Navier-Stokes Equations,"

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