Local Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations

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.

Automated summary

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