In this paper, we consider the classical solutions to a model of two-dimensional incompressible inviscid Boussinesq–Bénard equations. Notice that, in the case when the source term of temperature equation in this model is the second component of velocity \(u_2\) or no source term, there is no global-in-time existence result for the general initial data. Here, if the source term is only chosen as \(\Delta u_2\), then we can obtain the global well-posedness, inviscid limit and some exponential decay estimates. Our key observation is the nice symmetrical structure hidden in the corresponding system, which plays an extremely important role in the global well-posedness studied here.

在本文中，我们考虑了二维不可压缩的无粘性Boussinesq–Bénard方程模型的经典解。请注意，在此模型中温度方程的源项是速度\（u_2 \）的第二分量或没有源项的情况下，对于一般初始数据，没有全局时间存在性结果。在这里，如果仅将源项选择为\（\ Delta u_2 \），则可以获得整体的适定性，无粘性极限和一些指数衰减估计。我们的主要观察结果是隐藏在相应系统中的良好对称结构，该结构在此处研究的总体适度性中起着极其重要的作用。