We study the Cauchy problem of the three-dimensional full compressible Euler equations with damping and heat conduction. We prove the existence and uniqueness of the global small solution; in particular, we only require that the norms of the initial data be small when . Moreover, we use a pure energy method to show that the global solution converges to the constant equilibrium state with an optimal algebraic decay rate as time goes to infinity.

中文翻译：

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具阻尼和热传导的完全可压缩Euler方程解的整体存在性和长时间行为。

我们研究了具有阻尼和热传导的三维完全可压缩Euler方程的Cauchy问题。我们证明了全球小型企业的存在和独特性解决方案; 特别是，我们仅要求在以下情况下初始数据的规范要小。此外，我们使用一种纯能量方法来证明随着时间趋于无穷大，整体解以最佳的代数衰减率收敛到恒定的平衡状态。