journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2181 A new regularity criterion for the 3D-Boussinesq equations in homogeneous Besov and Triebel-Lizorkin spaces Benallia Mohamed Department of Mathematics, École Normale Supérieure de Bousaada, Bousaada, 28001, Algeria Laboratoire de Mathématiques et Physique Appliquées, École Normale Supérieure de Bousaada, Laboratory of Functional Analysis and Geometry of Spaces, Road Bourdj Bou Arreiridj, University of M’sila, M’sila, 28000, Algeria Dilmi Mohamed Department of Mathematics, LAMDA-RO Laboratory, BP 270 Soumâa Rd-Blida, University Saad Dahlab Blida 1, Algeria 28 5 1931 1939 13 08 2025

This paper aims to establish a new regularity criterion for weak solutions to the three-dimensional (3D) Boussinesq equations in the homogeneous Besov spaces Ḃsp,q (ℝ3) and the homogeneous Triebel–Lizorkin spaces Ḟsp,q (ℝ3). This regularity is proven if the velocity ω satisfies the following condition  ∫I ||ω||2Ḃp,q (ℝ3)2 dt

 Besov and Triebel-Lizorkin spaces Regularity criterion 3D-Boussinesq equations access open retracted no