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Optimal 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
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand;Centre of Excellence in Mathematics, CHE, Bangkok, Thailand
- 1 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand;Centre of Excellence in Mathematics, CHE, Bangkok, Thailand
Applied Mathematics·Volume 04 (2013)·Pages 1154–1162·Published 23 July 2013·DOI10.4236/am.2013.48154
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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 ((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.
KeywordsOptimal SystemInvariant SolutionsPartially Invariant SolutionsNavier-Stokes Equations
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