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<p>We study the essential spectrum, which corresponds to inertia–gravity modes, of the system of equations governing a rotating and self-gravitating gas planet. With certain boundary conditions, we rigorously and precisely characterize the essential spectrum and show how it splits from the portion of the spectrum corresponding to the acoustic modes. The fundamental mathematical tools in our analysis are a generalization of the Helmholtz decomposition and the Lopantinskii conditions.</p>

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Characterization of the spectra of rotating truncated gas planets and inertia–gravity modes

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  • 发表日期：

    2025年12月1日

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  • Maarten V. de Hoop,
  • Sean Holman

摘要

We study the essential spectrum, which corresponds to inertia–gravity modes, of the system of equations governing a rotating and self-gravitating gas planet. With certain boundary conditions, we rigorously and precisely characterize the essential spectrum and show how it splits from the portion of the spectrum corresponding to the acoustic modes. The fundamental mathematical tools in our analysis are a generalization of the Helmholtz decomposition and the Lopantinskii conditions.