Optimal System and Invariant Solutions on ((U_{yy}(t,s,y)－U_{t}(t,s,y))y－2sU_{sy}(t,s,y))y＋（s^{2}＋1)U_{ss}(t,s,y)＋2sU_{s}=0

Author(s)
Sopita Khamrod

Abstract

The purpose of this paper is to find the invariant solutions of the reduction of the Navier-Stokes equations where s=z/y ((U_{yy}(t,s,y)－U_{t}(t,s,y))y－2sU_{sy}(t,s,y))y＋（s^{2}＋1)U_{ss}(t,s,y)＋2sU_{s}=0 This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Group classification of the admitted Lie algebras of this equation is obtained. Two-dimensional optimal system is constructed from classification of their subalgebras. All invariant solutions corresponding to these subalgebras are presented.

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 and Invariant Solutions on ((U_{yy}(t,s,y)－U_{t}(t,s,y))y－2sU_{sy}(t,s,y))y＋（s^{2}＋1)U_{ss}(t,s,y)＋2sU_{s}=0," *Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 1154-1162. doi: 10.4236/am.2013.48154.

S. Khamrod, "Optimal System and Invariant Solutions on ((U

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