This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, are unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity.

中文翻译：

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三维可压缩本原方程强解的局部适定性

这项工作致力于为大气动力学的三维可压缩原始方程建立强解的局部实时适定性。结果表明，在以下两种情况下，短时间内存在很强的解决方案，它们是唯一的，并且连续取决于初始数据：有重力但没有真空，有真空却没有重力。