Optimal System and Invariant Solutions on ((U&lt;sub&gt;yy&lt;/sub&gt;(t,s,y)－U&lt;sub&gt;t&lt;/sub&gt;(t,s,y))y－2sU&lt;sub&gt;sy&lt;/sub&gt;(t,s,y))y＋（s&lt;sup&gt;2&lt;/sup&gt;＋1)U&lt;sub&gt;ss&lt;/sub&gt;(t,s,y)＋2sU&lt;sub&gt;s&lt;/sub&gt;=0 | Zendy

Sopita Khamrod | Zendy

Open Access

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

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 ((U_yy(t,s,y)U_t(t,s,y))y2sU_sy(t,s,y))ys²1)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.