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<p>We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard well-posedness of global strong solutions to this model. The lack of thermal diffusion introduces significant challenges in the analysis. To overcome these challenges, we first investigate the regularized model with thermal diffusion and establish delicate estimates that are independent of the thermal diffusion coefficient, and consequently justify the vanishing diffusivity limit. This work serves as a continuation of our previous paper Cao et al. (J. Evol. Equ. 21:2923–2954 (2021)).</p>

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Analysis of a Three-Dimensional Rapidly Rotating Convection Model Without Thermal Diffusion

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Chongsheng Cao,
  • Yanqiu Guo,
  • Edriss S. Titi

摘要

We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard well-posedness of global strong solutions to this model. The lack of thermal diffusion introduces significant challenges in the analysis. To overcome these challenges, we first investigate the regularized model with thermal diffusion and establish delicate estimates that are independent of the thermal diffusion coefficient, and consequently justify the vanishing diffusivity limit. This work serves as a continuation of our previous paper Cao et al. (J. Evol. Equ. 21:2923–2954 (2021)).