Stability of purely convective steady-states of fractional Boussinesq equations in an exterior domain

TL;DR

This paper investigates the stability of purely convective steady states in a 3D exterior domain with fractional viscosity, establishing the existence of weak solutions and their global stability.

Contribution

It introduces a fractional Boussinesq model in an exterior domain and proves the global stability of steady states, extending classical results to fractional viscosity settings.

Findings

Existence of weak solutions for the fractional Boussinesq equations.

Global stability of the steady-state solution in L^2.

Analysis in an unbounded exterior domain.

Abstract

A thermal convection flow in the three-dimensional unbounded fluid domain exterior to a sphere is considered. The viscosity force is determined by a fractional power of the Stokes operator. A purely conductive steady state arises due to the fluid heated from the sphere. A weak solution of the fluid motion problem is obtained and global stability of the steady-state solution in $L^2$ is provided.