Navier-Stokes equations under Marangoni boundary conditions generate all hyperbolic dynamics
arXiv:1511.02047
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 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.