Well-posedness of Hibler's dynamical sea-ice model

TL;DR

This paper proves the local-in-time well-posedness of a regularized version of Hibler's sea-ice model, ensuring mathematical soundness for simulations and future analysis of Arctic ice dynamics.

Contribution

It establishes the well-posedness of a carefully regularized, coupled hyperbolic-parabolic sea-ice model, bridging the gap between numerical simulations and theoretical understanding.

Findings

Proves local-in-time existence and uniqueness of solutions.

Designs a physically motivated regularization preserving model structure.

Provides a foundation for numerical and analytical studies of sea-ice dynamics.

Abstract

This paper establishes the local-in-time well-posedness of solutions to an approximating system constructed by mildly regularizing the dynamical sea-ice model of {\it W.D. Hibler, Journal of Physical Oceanography, 1979}. Our choice of regularization has been carefully designed, prompted by physical considerations, to retain the original coupled hyperbolic-parabolic character of Hibler's model. Various regularized versions of this model have been used widely for the numerical simulation of the circulation and thickness of the Arctic ice cover. However, due to the singularity in the ice rheology, the notion of solutions to the original model is unclear. Instead, an approximating system, which captures current numerical study, is proposed. The well-posedness theory of such a system provides a first-step groundwork in both numerical study and future analytical study.