Strong solutions of fractional Boussinesq equations in an exterior domain

TL;DR

This paper proves the existence of strong solutions for fractional Boussinesq equations in an exterior domain, demonstrating local stability of the steady state in a 3D thermal convection model.

Contribution

It introduces a fractional equation system for exterior domain thermal convection and establishes the existence of small strong solutions in a Hilbert space.

Findings

Existence of small strong solutions in an exterior domain

Steady state is locally stable and asymptotically attracting

Fractional equations effectively model thermal convection in exterior regions

Abstract

A thermal convection fluid motion in the three-dimensional domain exterior to a sphere is considered. A purely conductive steady state arises due to the fluid heated from the sphere. A fractional equation system is introduced by using spectral presentation. The existence of small strong solutions in a Hilbert space is obtained. The strong solution existence implies the local stability of the steady state, which attracts asymptotically the flows evolving initially from the vector fields close to the steady state.