On the Singular Limit in Hibler's Sea Ice Model

TL;DR

This paper proves the existence of energy-driven solutions to Hibler's sea ice model's momentum equation, addressing the singular limit and unregularized stress, and introduces a new solution concept capturing plasticity effects.

Contribution

It introduces an energy-based solution framework for Hibler's model that handles the singular limit and unregularized stress, with novel boundary term approximation and reduction schemes.

Findings

Established existence of energy-driven solutions for Hibler's model.

Developed a reduction scheme for nonlinear trace expressions.

Classified solutions applicable to non-constant mass cases.

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.