Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel

TL;DR

This paper proves the existence and regularity of a global attractor for the Newton-Boussinesq equation in a 2D channel, demonstrating its long-term bounded behavior through uniform tail estimates.

Contribution

It establishes the existence, asymptotic compactness, and regularity of the global attractor for the Newton-Boussinesq equation in a two-dimensional channel, advancing understanding of its long-term dynamics.

Findings

Existence of a global attractor for the equation

Asymptotic compactness via uniform tail estimates

Regularity of the global attractor

Abstract

We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.