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Optimal System and Invariant Solutions on ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=0

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DOI: 10.4236/am.2013.48154    2,539 Downloads   4,193 Views  
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ABSTRACT

The purpose of this paper is to find the invariant solutions of the reduction of the Navier-Stokes equations where s=z/y ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Khamrod, "Optimal System and Invariant Solutions on ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=0," Applied Mathematics, Vol. 4 No. 8, 2013, pp. 1154-1162. doi: 10.4236/am.2013.48154.

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