Zero Mach Number Limit of the Compressible Primitive Equations: Well-Prepared Initial Data

Abstract

Funder: Einstein Stiftung Berlin; doi: http://dx.doi.org/10.13039/501100006188Funder: John Simon Guggenheim Memorial Foundation; doi: http://dx.doi.org/10.13039/100005851This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data (i.e., initial data without acoustic oscillations) is rigorously justified, and the convergence rate is shown to be of order $\mathcal O(\varepsilon)$, as $\varepsilon \rightarrow 0^+$, where $\varepsilon$ represents the Mach number. As a byproduct, we construct a class of global solutions to the compressible primitive equations, which are close to the incompressible flows