We study the low Mach number limit of the full Navier–Stokes–Fourier system in the case of low stratification with ill-prepared initial data for the problem stated on a moving domain with a prescribed motion of the boundary. Similarly as in the case of a fixed domain, we recover as a limit the Oberback–Boussinesq system; however, we identify one additional term in the temperature equation of the limit system which is related to the motion of the domain and which is not present in the case of a fixed domain. One of the main ingredients in the proof is the properties of the Helmholtz decomposition on moving domains and the dependence of eigenvalues and eigenspaces of the Neumann Laplace operator on time.

我们研究了在低分层情况下，对于准备在边界上有规定运动的运动域中提出的问题的初始数据准备不充分的低分层情况下，整个Navier–Stokes–Fourier系统的低马赫数极限。与固定域类似，我们将Oberback–Boussinesq系统作为极限进行恢复；但是，我们在极限系统的温度方程中确定了一个与畴的运动有关的附加项，而在固定畴的情况下则不存在。证明中的主要成分之一是亥姆霍兹分解在移动域上的性质以及Neumann Laplace算子的特征值和特征空间对时间的依赖性。