The finite dimensions and determining modes of the global attractor for 2d Boussinesq equations with fractional Laplacian

TL;DR

This paper proves that the 2D Boussinesq system with fractional Laplacian has a finite-dimensional global attractor and estimates the number of determining modes, advancing understanding of its long-term dynamics.

Contribution

It establishes the finite dimensionality of the global attractor and provides estimates for the determining modes in the 2D Boussinesq system with fractional Laplacian.

Findings

Global attractor is finite dimensional.

Number of determining modes is estimated.

Results apply to subcritical fractional Laplacian case.

Abstract

In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case.