Abstract In this paper we consider the Cauchy problem of a model of the two-dimensional zero diffusivity Boussinesq equations with temperature-dependent viscosity. We show that there is a unique global smooth solution to this system for arbitrarily large initial data in Sobolev spaces. Our key argument is the De Giorgi-Nash-Moser estimates for the vorticity equation.

中文翻译：

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无扩散系数的二维温度相关 Boussinesq 方程模型的全局适定性

摘要 在本文中，我们考虑了具有温度相关粘度的二维零扩散系数 Boussinesq 方程模型的柯西问题。我们表明，对于 Sobolev 空间中任意大的初始数据，该系统有一个独特的全局平滑解。我们的关键论点是涡度方程的 De Giorgi-Nash-Moser 估计。