Navier-Stokes equations under Marangoni boundary conditions generate all hyperbolic dynamics

Abstract

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.