Well-posedness of Hibler's parabolic-hyperbolic sea ice model

TL;DR

This paper establishes the local-in-time well-posedness of a regularized Hibler's sea ice model, using advanced mathematical techniques to handle hyperbolic terms and prove strong solutions in a climate science context.

Contribution

It proves the well-posedness of a parabolic-hyperbolic regularized version of Hibler's sea ice model, employing Lagrangian coordinates and maximal regularity methods.

Findings

Proves local-in-time strong well-posedness of the model.

Uses Lagrangian coordinates to manage hyperbolic terms.

Establishes maximal L^p-regularity for the linearized problem.

Abstract

This paper proves the local-in-time strong well-posedness of a parabolic-hyperbolic regularized version of Hibler's sea ice model. Hibler's model is the most frequently used sea ice model in climate science. Lagrangian coordinates are employed to handle the hyperbolic terms in the balance laws. The resulting problem is regarded as a quasilinear non-autonomous evolution equation. Maximal $\mathrm{L}^p$-regularity of the underlying linearized problem is obtained on an anisotropic ground space in order to deal with the lack of regularization in the balance laws.