Article citationsMore>>

B. J. Cantwell, “Similarity Transformations for the Two Dimensional, Unsteady, Stream-Function Equation,” Jour nal of Fluid Mechanics, Vol. 85, No. 2, 1978, pp. 257-271. doi:10.1017/S0022112078000634

has been cited by the following article:

• TITLE: 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

  AUTHORS: Sopita Khamrod

  KEYWORDS: Optimal System; Invariant Solutions; Partially Invariant Solutions; Navier-Stokes Equations

  JOURNAL NAME: Applied Mathematics, Vol.4 No.8, July 30, 2013

  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.