Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation

Atanas Stefanov; Jiahong Wu; Xiaojing Xu; Zhuan Ye

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arXiv · 2606.03680

Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation

Atanas Stefanov·Jiahong Wu·Xiaojing Xu·Zhuan Ye

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Abstract

This paper studies the global regularity problem for the two-dimensional incompressible Boussinesq equations with fractional dissipation given by $(-Δ)^{\frac\alpha2}u$ and $(-Δ)^{\frac\beta2} θ$. Attention is focused on the subcritical regime where $α+ β>1$. The case $α>\frac23$ was recently settled in a joint work of the authors [Math. Ann., \textbf{391} (2025), 5965-6012], which established global regularity under this condition. This paper addresses the remaining case $α\leq \frac23$. We obtain the sharpest regularity result by minimizing assumptions on $α$ and $β$. We derive nonlinear lower bounds for the fractional Laplacian operator and implement an iterative procedure.

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BibTeX RIS

Atanas Stefanov, Jiahong Wu, Xiaojing Xu, Zhuan Ye. 2026-06-02. Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation. https://arxiv.org/abs/2606.03680

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