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<p>We establish uniform with respect to the Mach number estimates for local strong solution to the compressible primitive equations with gravity. 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, the uniform estimates are not easy to be constructed and some novel techniques are required. Using the estimates, we justify the low Mach number limit of the system with well-prepared initial data and obtain the convergence rate which is identical to the Mach number.</p>

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Uniform estimates for the compressible primitive equations with gravity and low Mach number

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Pengcheng Mu

摘要

We establish uniform with respect to the Mach number estimates for local strong solution to the compressible primitive equations with gravity. 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, the uniform estimates are not easy to be constructed and some novel techniques are required. Using the estimates, we justify the low Mach number limit of the system with well-prepared initial data and obtain the convergence rate which is identical to the Mach number.