Analysis of a Viscoplastic Burgers Equation

Abstract

We study a Burgers equation featuring an additional stress term that is governed by a positively -homogeneous potential. This problem is motivated by the so-called Hibler's sea ice model, which treats sea ice as a non-Newtonian fluid, where the stress tensor includes such a term in order to account for the plastic response of the ice. We present analytical results on Hibler's sea ice model and for the simplified model given by the viscoplastic Burgers equation. In particular, we introduce a suitable notion of weak solution, study their existence, and further discuss their properties.