A mathematical study of an elastic-viscous-plastic sea-ice model with the Kelvin-Voigt rheology

TL;DR

This paper develops and analyzes a Kelvin-Voigt regularized elastic-viscous-plastic sea-ice model, proving well-posedness and establishing new estimates, advancing mathematical understanding of sea-ice dynamics in climate models.

Contribution

It introduces a Kelvin-Voigt regularization in the momentum balance of the EVP sea-ice model and proves well-posedness results, including for less regular initial data.

Findings

Proved local and global well-posedness of the Kelvin-Voigt EVP model.

Established a new $L^inity$-estimate for the stress tensor.

Handled viscosity coefficients without an upper cutoff, addressing a major open problem.

Abstract

Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations, we proposed in [D. W. Boutros, X. Liu, M. Thomas and E. S. Titi, arXiv:2505.03080 (2025)] the use of the inviscid Voigt regularisation for the constitutive (stress-tensor) relation and proved the global well-posedness of the resulting model. The EVP model treats sea ice as a non-Newtonian fluid. In turn, elastic-viscous-plastic solids often involve a Kelvin-Voigt viscosity in terms of the strain rate. Therefore, in the present work we formulate an elastic-viscous-plastic sea-ice model with a Kelvin-Voigt regularisation in terms of the strain rate. In other words, we introduce the Voigt regularisation in the momentum balance rather than in the constitutive relation (for the stress tensor). We then prove the local well-posedness for the Kelvin-Voigt EVP model with the advection term, in the momentum balance, and the global well-posedness in the absence of the advection term (following a very standard approximation in the latter case). A crucial component of the proof of these results, is a new $L^\infty$-estimate for the stress tensor which relies on the damping structure. Note that, both with and without the advection term, we are able to handle the case of viscosity coefficients without a cutoff from above, which remains a major open problem for the closely related Hibler sea-ice model. We are also able to prove the existence of solutions for much less regular initial data compared to our previous paper on the Voigt-EVP model.