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arXiv · 2512.06202

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

Matthias Hieber·Igor Kukavica·Amjad Tuffaha·Qi Xu
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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.

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Matthias Hieber, Igor Kukavica, Amjad Tuffaha, Qi Xu. 2025-12-05. A geophysical free-boundary system modeling an ice-sheet interacting with an ocean. https://arxiv.org/abs/2512.06202

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