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

Sopita Khamrod

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand&Centre of Excellence in Mathematics, CHE, Bangkok, Thailand.

**DOI: **10.4236/am.2013.41022
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Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand&Centre of Excellence in Mathematics, CHE, Bangkok, Thailand.

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

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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