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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    2,440 Downloads   4,015 Views  
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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.

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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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