The Oberbeck-Boussinesq system with non-local boundary conditions

TL;DR

This paper studies the Oberbeck-Boussinesq system with non-local boundary conditions, establishing the existence of strong solutions and showing global existence in two dimensions, as a limit of the Navier-Stokes-Fourier system.

Contribution

It introduces a new analysis of the Oberbeck-Boussinesq system with non-local boundary conditions, including existence results and global solutions in 2D.

Findings

Existence of strong solutions on a maximal time interval.

Global existence of solutions in two dimensions.

Connection to the singular limit of Navier-Stokes-Fourier system.

Abstract

We consider the Oberbeck--Boussinesq system with non--local boundary conditions arising as a singular limit of the full Navier--Stokes--Fourier system in the regime of low Mach and low Froude number. The existence of strong solutions is shown on a maximal time interval $[0, T_{\rm max})$. Moreover, $T_{\rm max} = \infty$ in the two dimensional setting.