The Oberbeck-Boussinesq system with non-local boundary conditions

2022/06/30 by Anna Abbatiello, Eduard Feireisl, Abbatiello, Anna +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.15130

openalex publication_date 2022/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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} = ∞ in the two dimensional setting.

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