Universal dynamical approximation by Oberbeck-Boussinesque model

We consider dynamics defined by the Navier–Stokes equations in the Oberbeck–Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involves fundamental physical effects: convection and diffusion. The main result is as follows: local semiflows, induced by this problem, can generate all possible structurally stable dynamics defined by C1 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 viscosity coefficient, an external heat source, some parameters in boundary conditions and the small perturbation of the gravitational force.