# Strange attractors for Overbeck -Boussinesq model

## TL;DR

This paper demonstrates that the two-dimensional Oberbeck-Boussinesq model of fluid dynamics can produce any structurally stable dynamics on compact manifolds by adjusting physical parameters, highlighting its versatile dynamical capabilities.

## Contribution

It shows that the Navier-Stokes equations under the Oberbeck-Boussinesq approximation can generate all structurally stable dynamics through parameter tuning.

## Key findings

- Local semiflows can generate all structurally stable dynamics.
- Adjusting parameters like viscosity and heat sources can produce desired dynamics.
- The model encompasses a wide range of dynamical behaviors.

## Abstract

In this paper, we consider dynamics defined by the Navier-Stokes equations in the Oberbeck-Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involve 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 $C^1$ smooth vector fields on compact smooth manifolds (up to an orbital topological equivalency). 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.