On the attractor of the semi-dissipative Boussinesq equations revised

Kexin Li; Chunyou Sun

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arXiv · 2607.22107

On the attractor of the semi-dissipative Boussinesq equations revised

Kexin Li·Chunyou Sun

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Abstract

In this paper, we continue investigate the structure of the weak $\sigma$-attractor $\mathcal{A}$ for the 2D Boussinesq equations with viscosity and without heat diffusion. Specifically, we show that the projection of the attractor $\mathcal{A}$ onto the temperature component is surjective, i.e., $P_{\theta}\mathcal{A}=L^2$; and, for any $r>0$, the projection of $\mathcal{A}_r$ onto the velocity component contains a infinite-dimensional Hilbert ellipsoid, which implies $P_u\mathcal{A}_r$ is infinite dimensional immediately.

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Kexin Li, Chunyou Sun. 2026-07-24. On the attractor of the semi-dissipative Boussinesq equations revised. https://arxiv.org/abs/2607.22107

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