WELL-POSEDNESS RESULTS FOR A NONLINEAR STOKES PROBLEM ARISING IN GLACIOLOGY

We provide well-posedness results for a nonlinear, incompressible Stokes problem that models the flow of ice in glaciers and ice sheets, e. g., Greenland and Antarctica. An important feature of the problem, in addition to the highly nonlinear rhcology, are boundary conditions which describe the Coulomb-like friction at the ice-bedrock interface. Results available in the literature for similar nonlinear Stokes problems do not fully account for boundary conditions typical of glaciology. Most well-posedness results previously obtained deal with the elliptic Blatter-Pattyn model that is an approximation of the Stokes model. In this work, we consider the boundary conditions proposed by Schoof and extend his well-posendess results to the Stokes case. Difficulties in the analysis of the Stokes model are generated by the fact that boundary conditions can possibly depend on the normal stress. In this case, led by arguments typical in the linear elasticity context, we prove an existence result for nonlocal friction boundary conditions. Moreover, following Schoof, we prove that the Coulomb friction problem can be approximated by differentiable boundary conditions that render numerical simulations more affordable.