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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 ()

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.

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_{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.

Conflicts of Interest

The authors declare no conflicts of interest.

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