In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the time-independent lower-order and time-dependent higher-order a priori estimates, we prove that the classical solution exists globally in time provided the initial mass $\|\rho _{0}\|_{L^{1}}$ of the fluid is small. Here, we have no small requirements for the initial velocity and temperature.

中文翻译：

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平方域中二维可压缩Boussinesq方程经典解的整体存在

在本文中，我们考虑具有恒定粘度和热扩散系数的二维等熵可压缩Boussinesq方程在平方域中的初边值问题。基于与时间无关的低阶和与时间有关的高阶的先验估计，我们证明了经典解决方案在初始质量$ \ | \ rho _ {0} \ | _ {L ^ { 1}} $的流体很小。在这里，我们对初始速度和温度有不小的要求。