Open AccessOptimal System and Invariant Solutions on ((U<sub>yy</sub>(t,s,y)－U<sub>t</sub>(t,s,y))y－2sU<sub>sy</sub>(t,s,y))y＋（s<sup>2</sup>＋1)U<sub>ss</sub>(t,s,y)＋2sU<sub>s</sub>=0
Author(s) -
Sopita Khamrod
Publication year - 2013
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2013.48154
Subject(s) - invariant (physics) , ampere , mathematics , mathematical physics , physics , mathematical analysis , thermodynamics , current (fluid)
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))y2sUsy(t,s,y))ys21)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.