In this paper, we consider a three-dimensional compressible viscous heat-conducting fluid in a horizontally periodic domain, bounded above by a free surface and below by a rigid bottom. The motion of the fluid is governed by the full compressible, gravity-driven Navier–Stokes equations with appropriate boundary conditions. On the free surface, the effect of surface tension is neglected, and the temperature is assumed to satisfy the Robin boundary condition. Motivated by Y. Guo and I. Tice [Anal. PDE 6, 287–369 (2013), Arch. Ration. Mech. Anal. 207, 459–531 (2013), and Anal. PDE 6, 1429–1533 (2013)], we establish the global well-posedness of this free boundary problem, provided that the initial data are close to a nontrivial equilibrium state.

中文翻译：

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无表面张力的可压缩粘性导热表面波

在本文中，我们考虑水平周期域中的三维可压缩粘性导热流体，其上界为自由表面，下界为刚性底部。流体的运动由具有适当边界条件的完全可压缩、重力驱动的 Navier-Stokes 方程控制。在自由表面上，忽略表面张力的影响，假设温度满足 Robin 边界条件。由 Y. Guo 和 I. Tice 推动 [Anal. PDE 6 , 287–369 (2013), Arch。配给。机械。肛门。207 , 459–531 (2013) 和肛门。PDE 6 , 1429–1533 (2013)]，我们建立了这个自由边界问题的全局适定性，前提是初始数据接近非平凡的平衡状态。