variavel0=<b>Atila P. Silva Freire</b> - atila@serv.com.ufrj.br PEM/COPPE/UFRJ
<b>Juliana B. R. Loureiro</b> - jbrloureiro@serv.com.ufrj.br DEM/EE/UFRJ
<b>Abstract.</b> In the present work,some formal properties of singular perturbation equations are studied through the concept of "equivalent in the limit" of Kaplun,so that a proposition for the principal equations is derived.The proposition shows that if there is a principal equation at a point (n,1) of the (X × E) product space, X space of all positive continuous functions in (0 ,1 ], E=(0 ,1], then there is also a principal equation at a point (n, e) of (X × E), e=first critical order. The converse is also true.The proposition is of great implication for it ensures that the asymptotic structure of a singular perturbation problem can be determined by a first order analysis of the formal domains of validity.The turbulent boundary layer asymptotic structure is then studied by application of Kaplun limits to the near region of the leading edge of a flat plate.As it turns out,a different asymptotic structures is found from those previously deduced by other authors; in fact the results show that a ulti-layered structure exists near the leading edge which,however,is different fro the classical structure commonlyfound in literature.
<b>Keywords.</b> Kaplun limits, Asymptotic methods, Leading edge.