The goal of this paper is to study the two-dimensional inviscid Boussinesq equations with temperature-dependent thermal diffusivity. Firstly we establish the global existence theory and regularity estimates for this system with Yudovich's type initial data. Then we investigate the vortex patch problem, and proving that the patch remains in Hölder class $ C^{1+s}\; (0<s<1) $ for all the time.

中文翻译：

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关于具有热扩散率的二维Boussinesq系统的Yudovich型解

本文的目的是研究具有温度依赖性热扩散率的二维无粘性Boussinesq方程。首先，我们利用尤多维奇类型的初始数据建立了该系统的整体存在性理论和规律性估计。然后，我们研究涡旋斑块问题，并证明该斑块仍处于Hölder类$ C ^ {1 + s} \;中。始终（0 <s <1）$。