Geometric inverse problems on gas giants
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913258334584832 |
|---|---|
| author | de Hoop, Maarten V. Ilmavirta, Joonas Kykkänen, Antti Mazzeo, Rafe |
| author_facet | de Hoop, Maarten V. Ilmavirta, Joonas Kykkänen, Antti Mazzeo, Rafe |
| contents | On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: the boundary is at a finite distance.
We study the differential geometry of such manifolds, especially the asymptotic behavior of geodesics near the boundary. We relate the geometry to the propagation of singularities of a hydrodynamic PDE and we give the basic properties of the Laplace--Beltrami operator. We solve two inverse problems, showing that the interior structure of a gas giant is uniquely determined by different types of boundary data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric inverse problems on gas giants de Hoop, Maarten V. Ilmavirta, Joonas Kykkänen, Antti Mazzeo, Rafe Differential Geometry Analysis of PDEs 53C22, 37D40, 53C65, 35R30 On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: the boundary is at a finite distance. We study the differential geometry of such manifolds, especially the asymptotic behavior of geodesics near the boundary. We relate the geometry to the propagation of singularities of a hydrodynamic PDE and we give the basic properties of the Laplace--Beltrami operator. We solve two inverse problems, showing that the interior structure of a gas giant is uniquely determined by different types of boundary data. |
| title | Geometric inverse problems on gas giants |
| topic | Differential Geometry Analysis of PDEs 53C22, 37D40, 53C65, 35R30 |
| url | https://arxiv.org/abs/2403.05475 |