The global attractor of the 2D Boussinesq equations with fractional Laplacian in Subcritical case

TL;DR

This paper establishes the global existence of solutions and a global attractor for the 2D Boussinesq equations with fractional Laplacian in a periodic domain, highlighting the influence of the fractional exponent on solution regularity.

Contribution

It proves global well-posedness and existence of a global attractor for the 2D Boussinesq system with fractional Laplacian in the subcritical case, linking the Laplacian exponent to regularity.

Findings

Global well-posedness of strong solutions

Existence of a global attractor

Relationship between Laplacian exponent and regularity

Abstract

We prove global well-posedness of strong solutions and existence of the global attractor for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and temperature.