WIAS Preprint No. 2833, (2021)

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


Authors

  • Liu, Xin
    ORCID: 0000-0001-7021-8644
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X
  • Titi, Edriss
    ORCID: 0000-0002-5004-1746

2020 Mathematics Subject Classification

  • 35A01 35A02 35Q86 86A05

Keywords

  • Well-posedness, ice rheology, sea-ice, Hibler sea-ice model

DOI

10.20347/WIAS.PREPRINT.2833

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.

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