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

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.