This article studies the global regularity problem of the two‐dimensional zero thermal diffusion tropical climate model with fractional dissipation, given by ${(-\mathrm{\Delta })}^{\alpha }u$ in the barotropic mode equation and by ${(-\mathrm{\Delta })}^{\beta }v$ in the first baroclinic mode of the vector velocity equation. More precisely, we show that the global regularity result holds true as long as $\alpha +\beta \ge 2$ with $1<\alpha <2$. In addition, with no dissipation from both the temperature and the first baroclinic mode of the vector velocity, we also establish the global regularity result with the dissipation strength at the logarithmically supercritical level. Finally, our arguments can be extended to obtain the corresponding global regularity results of the higher dimensional cases.

中文翻译：

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零热扩散的二维热带气候模型的整体规律

本文研究了具有零耗散的二维零热扩散热带气候模型的整体正则性问题，其公式为 ${（-\mathrm{\Delta }）}^{\alpha }ü$ 在正压模式方程中 ${（-\mathrm{\Delta }）}^{\beta }v$在矢量速度方程的第一个斜压模式下。更准确地说，我们证明，只要$\alpha +\beta \ge 2$ 与 $\mathrm{1个}<\alpha <2$。此外，在温度和矢量速度的第一个斜度模式都没有耗散的情况下，我们还建立了耗散强度处于对数超临界水平的全局规律性结果。最后，我们的论点可以扩展为获得高维情况的相应全局规则性结果。