On asymptotic stability of the 3D Boussinesq equations without thermal conduction

TL;DR

This paper proves that solutions to the 3D Boussinesq equations without thermal conduction, starting close to a stationary state, converge to it over time with explicit algebraic decay rates.

Contribution

It establishes the asymptotic stability of stationary solutions for the 3D Boussinesq equations without thermal conduction in a specific domain.

Findings

Solutions converge to stationary states with explicit algebraic rates.

Stability is proven for initial data near the stationary solution.

Results are valid in the domain rac12;rac12; imes (0,1).

Abstract

We investigate the asymptotic stability of solution to Boussinesq equations without thermal conduction with the initial data near a specific stationary solution in the three--dimensional domain $\Omega = \mathbb{R}^{2}\times (0,1)$. It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.