Regularity Criterion for the Three-dimensional Boussinesq Equations

2015/09/24 by Karen Zaya, Zaya, Karen
Engineering · Mathematics · #35Q35 (Secondary) #76D03 (Primary) #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.1509.07434

openalex publication_date 2015/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a solution to the three-dimensional Boussinesq equations does not blow-up at time T if ‖ u_{≤ Q}‖_B¹_{∞, ∞} is integrable on (0, T), where u_{≤ Q} represents the low modes of Littlewood-Paley projection of the velocity u.

Citations

• On the global well-posedness for Boussinesq system
• Global regularity for the 2D Boussinesq equations with partial viscosity terms

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