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Pré-Publication, Document De Travail Année : 2024

Weyl formulae for some singular metrics with application to acoustic modes in gas giants

Yves Colin de Verdìère
Charlotte Dietze
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Maarten V. de Hoop
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Résumé

This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with boundary whose metric blows up near the boundary. Here, the spectral analysis of the corresponding Laplace-Beltrami operator is presented and the Weyl law is derived. The involved exponents depend on the Hausdorff dimension which, in the supercritical case, is larger than the topological dimension.
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Dates et versions

hal-04627841 , version 1 (27-06-2024)

Identifiants

  • HAL Id : hal-04627841 , version 1

Citer

Yves Colin de Verdìère, Charlotte Dietze, Maarten V. de Hoop, Emmanuel Trélat. Weyl formulae for some singular metrics with application to acoustic modes in gas giants. 2024. ⟨hal-04627841⟩
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