Local Well-posedness of Strong Solutions to the Three-dimensional Compressible Primitive Equations

TL;DR

This paper proves the local existence, uniqueness, and continuous dependence of strong solutions to the 3D compressible primitive equations in atmospheric dynamics, considering cases with gravity and vacuum, and introduces a free boundary problem.

Contribution

It establishes the local well-posedness of strong solutions for the 3D compressible primitive equations, including new cases with vacuum and free boundary conditions.

Findings

Strong solutions exist and are unique for short times.

Solutions depend continuously on initial data.

Introduces a free boundary problem for these equations.

Abstract

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, 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. We also introduce the free boundary problem for the compressible primitive equations.