English

Strange attractors for Overbeck -Boussinesq model

Mathematical Physics 2019-01-08 v1 math.MP

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 C1C^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.

Keywords

Cite

@article{arxiv.1901.01254,
  title  = {Strange attractors for Overbeck -Boussinesq model},
  author = {Sergey Vakulenko},
  journal= {arXiv preprint arXiv:1901.01254},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1511.02047