In this paper we prove the local well-posedness and global well-posedness with small initial data of the strong solution to the reduced 3D primitive geostrophic adjustment model with weak dissipation. The term reduced model means that the relevant physical quantities depend only on two spatial variables. The weak dissipation helps us overcome the ill-posedness of the original model. We also prove the global well-posedness of the strong solution to the Voigt \(\alpha \)-regularization of this model, and establish the convergence of the strong solution of the Voigt \(\alpha \)-regularized model to the corresponding solution of the original model. Furthermore, we derive a criterion for existence of finite-time blow-up of the original model with weak dissipation based on Voigt \(\alpha \)-regularization.

中文翻译：

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耗散性降低的3D本构地转调整模型的适定性

在本文中，我们用弱耗散的简化3D原始地转调节模型的强解的强初始解的少量初始数据证明了局部适定性和全局适定性。术语简化模型意味着相关的物理量仅取决于两个空间变量。弱耗散有助于我们克服原始模型的不适。我们还证明了该模型的Voigt \（\ alpha \）正则化强解的全局适定性，并建立了Voigt \（\ alpha \）强解的收敛性-正规化模型到原始模型的相应解决方案。此外，我们基于Voigt \（\ alpha \） -正则化导出了具有弱耗散性的原始模型的有限时间爆燃的存在准则。