On the Singular Limit in Hibler's Sea Ice Model
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914153545859072 |
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| author | Denk, Robert Gmeineder, Franz Hieber, Matthias |
| author_facet | Denk, Robert Gmeineder, Franz Hieber, Matthias |
| contents | We establish the existence of energy-driven solutions to the momentum balance equation in Hibler's sea ice model. As a main novelty and different from previous results, we deal with the singular limit and therefore cover the true unregularized Hibler stress. To this end, we introduce an energy-based notion of solution that is able to capture plasticity effects of sea ice. This requires certain relaxations of the Hibler energies and, by the different function space set-up, comes with novel challenges. In particular, we establish a bulk approximation result of the boundary terms in the evolutionary relaxed Hibler energies. This is achieved by developing a novel reduction scheme for nonlinear trace expressions which should be of independent interest. Finally, based on our main results, we classify our findings within a broader concept of solutions that is applicable to the non-constant mass case too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Singular Limit in Hibler's Sea Ice Model Denk, Robert Gmeineder, Franz Hieber, Matthias Analysis of PDEs We establish the existence of energy-driven solutions to the momentum balance equation in Hibler's sea ice model. As a main novelty and different from previous results, we deal with the singular limit and therefore cover the true unregularized Hibler stress. To this end, we introduce an energy-based notion of solution that is able to capture plasticity effects of sea ice. This requires certain relaxations of the Hibler energies and, by the different function space set-up, comes with novel challenges. In particular, we establish a bulk approximation result of the boundary terms in the evolutionary relaxed Hibler energies. This is achieved by developing a novel reduction scheme for nonlinear trace expressions which should be of independent interest. Finally, based on our main results, we classify our findings within a broader concept of solutions that is applicable to the non-constant mass case too. |
| title | On the Singular Limit in Hibler's Sea Ice Model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.09327 |