On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces

TL;DR

This paper investigates the mathematical properties of the 2D Boussinesq equations with temperature-dependent diffusion coefficients, focusing on existence, uniqueness, and regularity in Sobolev spaces.

Contribution

It establishes existence, uniqueness, and regularity results for these equations in general Sobolev spaces, considering optimal regularity exponents.

Findings

Proved existence and uniqueness of solutions.

Analyzed regularity in Sobolev spaces.

Identified optimal regularity exponent ranges.

Abstract

We study the existence, uniqueness as well as regularity issues for the two-dimensional incompressible Boussinesq equations with temperature-dependent thermal and viscosity diffusion coefficients in general Sobolev spaces. The optimal regularity exponent ranges are considered.