TITLE:
Numerical study of bifurcations for the 2--D Poiseuille problem

AUTHORS:
Pablo S. Casas^(1), Angel Jorba^(2)

(1) Departament de Matem\`atica Aplicada I,
    Universitat Polit\`ecnica de Catalunya,
    Diagonal 647, 08028 Barcelona (Spain).

(2) Departament de Matem\`atica Aplicada i An\`alisi,
    Universitat de Barcelona,
    Gran Via 585, 08007 Barcelona (Spain).

E-mails: pablo@vilma.upc.es, angel@maia.ub.es

ABSTRACT:
We study the dynamics of two-dimensional Poiseuille flow.
Firstly we check our calculations with previous results concerning the
laminar solution and the minimum Reynolds number such that it becomes
unstable. Next we studied time periodic solutions which, because of the
imposed periodicity in the stream-wise direction, are rotating waves,
what allow us to treat them as stationary flows in a moving system of
reference. We use this fact to obtain also unstable time periodic flows
and bifurcation branches from the laminar solution for different values
of the wave number. Finally we introduce the case of bifurcation to
quasi-periodic solutions.
