We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken into account, and the density background profile is permitted to have physical vacuum singularity. The existing time of the solutions is infinite in two dimensions, with general initial data, and in three dimensions with small initial data.

中文翻译：

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层状粘滞流动非弹性方程强解的适定性

我们建立了分层粘性流的二维和三维非弹性方程的强解的局部和全局适定性。在该模型中，考虑了密度分布图与速度场的相互作用，并且允许密度背景分布图具有物理真空奇异性。解决方案的现有时间在二维范围内（具有一般初始数据）是无限的，而在三维范围内（具有较小的初始数据）是无限的。