The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity

TL;DR

This paper proves the global well-posedness and existence of a global attractor for strong solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity, under non-homogeneous boundary conditions.

Contribution

It establishes the well-posedness and attractor existence for the 2D Boussinesq system with temperature-dependent properties, extending previous results to more realistic variable coefficient models.

Findings

Global well-posedness of strong solutions is established.

Existence of a global attractor for the system is proved.

Results hold under non-homogeneous boundary conditions.

Abstract

Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved.