arXiv:2611.08765v1 Announce Type: new Abstract: In the present paper, our primary focus is on the Boussinesq equations with fractional velocity dissipation $\Lambda^\alpha u$ and temperature diffusion $\Lambda^\beta\theta$. On the critical balance line $\alpha+\beta=1$, establishing global regularity for weak velocity dissipation has been obstructed by the quadratic convective-buoyancy feedback, and all available results below $\alpha=\frac{10}{13}$ require a smallness assumption on the initial temperature. In this paper, we prove large-data global regularity across the extended regime $\alpha>\frac{\sqrt{57}-5}{4} \approx 0.637$. This provides a step beyond the previous barrier $\alpha=\frac{10}{13}$, unconditionally dismantling the temperature smallness assumption that has persisted in the literature for over a decade. The mathematical mechanism relies on a high-order Quadratic Normal Form transformation $H=\omega-R_{\alpha}\theta-\Bop(\theta,\theta)$ tailored to eliminate non-resonant quadratic vorticity-temperature interactions. Crucially, by uncovering the exact physical scalings of the underlying multilinear commutators and maintaining sharp fractional conjugates in the $L^m$-energy framework, we ensure that the global energy closure is governed entirely by the quadratic thermal dissipation. Once an integrability threshold $m>\frac{2}{\alpha}$ is attained, a fine Littlewood-Paley transport estimate drives a fractional regularity gain $H \in B_{r,\infty}^{3\alpha-2}$, ensuring the velocity field achieves critical drift regularity $C^{\alpha}$. By Silvestre-type drift regularization, this spontaneously generates positive H\"older continuity for the temperature, which in turn elevates the drift regularity strictly beyond the critical threshold, unlocking non-local Schauder estimates to prevent finite-time singularity formation.
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