A geophysical free-boundary system modeling an ice-sheet interacting with an ocean

TL;DR

This paper develops a mathematical model for ice-sheet and ocean interactions, capturing complex fluid-structure coupling and providing analytical estimates for solutions within a geophysical context.

Contribution

It introduces a novel free-boundary model using ALE formulation to analyze ice-ocean interactions with rigorous a priori estimates.

Findings

Established local-in-time existence of strong solutions.

Derived a priori estimates for nonlinear coupled system.

Addressed analytical challenges from high-order pressure terms.

Abstract

We consider a free-boundary model for the ice-sheet interacting with an ocean. The model captures the coupling between a viscous geophysical fluid and an elastic interface through kinematic and dynamic boundary conditions that account for hydrodynamic loading. Using the ALE formulation, we derive a system on a fixed reference domain and establish local-in-time a priori estimates for strong solutions with initial data in $H^2$. The main analytical difficulties arise from the nonlinear terms involving vertical derivatives and from high-order pressure contributions on the interface.