A logarithmically improved regularity criterion for the Boussinesq equations in a bounded domain

Ahmad M. Alghamdi (), Sadek Gala () and Maria Alessandra Ragusa ()
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Ahmad M. Alghamdi: Umm Alqura University
Sadek Gala: ENS of Mostaganem
Maria Alessandra Ragusa: Università di Catania

Partial Differential Equations and Applications, 2020, vol. 1, issue 6, 1-11

Abstract: Abstract The paper is concerned with the regularity of solutions of the Boussinesq equations for incompressible fluids without heat conductivity. The main goal is to prove a regularity criterion in terms of the vorticity for the initial boundary value problem in a bounded domain $$\Omega$$ Ω of $$\mathbb {R}^{3}$$ R 3 with Navier-type boundary conditions and we prove that if $$\begin{aligned} \int _{0}^{T}\frac{\left\| \omega (\cdot ,t)\right\| _{BMO(\Omega )}}{ \log \left( e+\left\| \omega (\cdot ,t)\right\| _{BMO(\Omega )}\right) }dt

Keywords: Boussinesq equations; Bounded domain; Smooth solutions; BMO spaces; 35Q35; 76D03 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00042-y

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