A regularity criterion for the 3D Boussinesq equations in homogeneous Besov spaces with negative indices

2024/01/17 by Mianlu Zou, Qiang Li, Zou, Mianlu +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2401.09219

openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the regularity criteria for the 3D Boussinesq equations in terms of one partial derivative of the velocity in Besov spaces. More precisely, it is proved that if the velocity u holds ∫₀^T‖ ∂₃ u‖_B_∞,∞^-r(2)/(1-r)dt<∞, with 0≤ r<1, then the solution (u, θ) is regular on [0,T].

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