  The dynamics defined by the Navier-Stokes equations under the Marangoni
boundary conditions in a two dimensional domain is considered. This model of
fluid dynamics involve fundamental physical effects: convection, diffusion and
capillary forces. The main result is as follows: local semiflows, defined by
the corresponding initial boundary value problem, can generate all possible
structurally stable dynamics defined by $C^1$ smooth vector fields on compact
smooth manifolds (up to an orbital topological equivalence). To generate a
prescribed dynamics, it is sufficient to adjust some parameters in the
equations, namely, the Prandtl number and an external heat source.
