Rigorous Analysis and Dynamics of Hibler's sea ice model

TL;DR

This paper provides a rigorous mathematical analysis of Hibler's sea ice model, establishing well-posedness results for the coupled velocity, thickness, and compactness equations within an $L_q$-framework.

Contribution

It is the first to rigorously analyze Hibler's sea ice model as a quasilinear evolution equation, proving local and global well-posedness results.

Findings

Model is locally strongly well-posed in $L_q$-setting

Model is globally strongly well-posed near constant equilibria

Hibler's ice stress identified as a quasilinear second order operator

Abstract

This article develops for the first time a rigorous analysis of Hibler's model of sea ice dynamics. Identifying Hibler's ice stress as a quasilinear second order operator and regarding Hibler's model as a quasilinear evolution equation, it is shown that Hibler's coupled sea ice model, i.e., the model coupling velocity, thickness and compactness of sea ice, is locally strongly well-posed within the $L_q$-setting and also globally strongly well-posed for initial data close to constant equilibria.