We establish a unique global strong solution for nonhomogeneous Bénard system with zero density at infinity on the whole two-dimensional (2D) space. In particular, the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies heavily on the structure of the system under consideration and spatial dimension.

中文翻译：

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具有大初始数据和真空的非齐次 Bénard 系统的全局强解

我们为整个二维 (2D) 空间上的无穷远零密度非齐次 Bénard 系统建立了独特的全局强解。特别是初始数据可以任意大，初始密度可以包含真空状态，甚至可以有紧致支撑。我们的方法在很大程度上依赖于所考虑系统的结构和空间维度。