In the work, we consider the zero Mach number limit of compressible primitive equations in the domain $\mathbb{ R}^2 \times 2\mathbb{ T}$ or $\mathbb{ T}^2 \times 2\mathbb{ T}$. We identify the limit equations to be the primitive equations with the incompressible condition. The convergence behaviors are studied in both $\mathbb{ R}^2 \times 2\mathbb{ T}$ and $\mathbb{ T}^2 \times 2\mathbb{ T}$, respectively. This paper takes into account the high oscillating acoustic waves and is an extension of our previous work by X. Liu and E.S. Titi, Arch. Rational Mech. Anal., 238, 705-747, 2020.
Categories: math.AP physics.ao-ph