Title: Low Mach number limit of strong solutions to the compressible primitive equations with gravity Show Chinese title

Title: 可压缩原始方程组在重力作用下强解的低马赫数极限

Abstract: In this paper, we explore the low Mach number singular limit of the local-in-time strong solutions to the compressible primitive equations with gravity for general adiabatic coefficient. First we construct the uniform estimate for the solutions to the non-dimensional compressible primitive equations with general ill-prepared initial data. Due to the effects of gravity and the anisotropy of the system, the operator with large coefficient in this model is not explicitly skew-symmetric. Thus, obtaining the uniform estimate requires novel techniques. After that, we investigate rigorously the low Mach number limit of the compressible primitive equations with both well-prepared and ill-prepared initial data. The limiting system is shown to be the incompressible primitive equations with inhomogeneous density that depends on the vertical variable. Show Chinese abstract

Abstract: 在本文中，我们探讨了具有重力的可压缩原始方程在一般绝热系数下的低马赫数奇异极限的局部时间强解。 首先，我们构建了非维可压缩原始方程在一般不良准备初始数据下的解的统一估计。 由于重力和系统的各向异性的影响，该模型中的大系数算子并不显式反对称。 因此，获得统一估计需要新的技术。 之后，我们严格研究了具有良好准备和不良准备初始数据的可压缩原始方程的低马赫数极限。 显示的极限系统是依赖于垂直变量的非均匀密度的不可压缩原始方程。