Global well-posedness of the elastic-viscous-plastic sea-ice model with the inviscid Voigt-regularisation

Abstract

In this paper, we initiate the rigorous mathematical analysis of the elastic-viscous-plastic (EVP) sea-ice model, which was introduced in [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849-1867]. The EVP model is one of the standard and most commonly used dynamical sea-ice models. We study a regularised version of this model. In particular, we prove the global well-posedness of the EVP model with the inviscid Voigt-regularisation of the evolution equation for the stress tensor. Due to the elastic relaxation and the Voigt regularisation, we are able to handle the case of viscosity coefficients without cutoff, which has been a major issue and a setback in the computational study and analysis of the related Hibler sea-ice model, which was originally introduced in [W. D. Hibler, J. Phys. Oceanogr., 9, 4 (1979), 815–846]. It is worth noting that the EVP model shares some structural characteristics with the Oldroyd-B model and related models for viscoelastic non-Newtonian complex fluids.