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arXiv · 2511.09327

On the Singular Limit in Hibler's Sea Ice Model

Robert Denk·Franz Gmeineder·Matthias Hieber
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Abstract

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.

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Robert Denk, Franz Gmeineder, Matthias Hieber. 2025-11-12. On the Singular Limit in Hibler's Sea Ice Model. https://arxiv.org/abs/2511.09327

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