A model of gravitational differentiation of compressible self-gravitating planets
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910690674999296 |
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| author | Mielke, Alexander Roubicek, Tomas Stefanelli, Ulisse |
| author_facet | Mielke, Alexander Roubicek, Tomas Stefanelli, Ulisse |
| contents | We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo-Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A model of gravitational differentiation of compressible self-gravitating planets Mielke, Alexander Roubicek, Tomas Stefanelli, Ulisse Analysis of PDEs 35Q49, 35Q74, 65M60, 74A30, 74L10, 76N06, 76T30, 86A17 We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo-Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions. |
| title | A model of gravitational differentiation of compressible self-gravitating planets |
| topic | Analysis of PDEs 35Q49, 35Q74, 65M60, 74A30, 74L10, 76N06, 76T30, 86A17 |
| url | https://arxiv.org/abs/2305.06232 |