  In most fluid dynamics problems, the governing equations are nonlinear
because of the presence of convective terms. Nevertheless, existence of
solutions can be shown by direct sum provided one identifies, in the relevant
Banach space of solutions, particular subspaces which are invariant under time
evolution. As an example, we consider classical convection problems and show
how symmetry arguments can help in identifying such subspaces, as well as the
role it can play in some stability issues.
