Weak Solutions for the Unregularised Hibler Momentum Equation with Degenerate Coefficients
Abstract
We study the momentum equation of the decoupled unregularised Hibler sea-ice model with non-negative ice mass and ice strength, both of which may vanish. The ocean drag provides coercivity, while the stress law and mixed boundary conditions are encoded by a convex dissipation functional. We prove existence, uniqueness and stability for the time-discrete problem and reconstruct an admissible stress. A Rothe approximation yields global weak variational solutions for time-dependent coefficients under a one-sided growth condition on the mass. Weak solutions are unique when the ice strength is independent of time. For spatially Lipschitz ice strength, finite dissipation also yields a local measure structure of the weighted deformation and a global bound on the negative part of the weighted divergence.
Related
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BibTeX
@misc{schneider2026weak,
title = {{Weak Solutions for the Unregularised Hibler Momentum Equation with Degenerate Coefficients}},
author = {Henrik Schneider},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12925},
eprint = {2609.12925},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12925},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weak Solutions for the Unregularised Hibler Momentum Equation with Degenerate Coefficients
AU - Henrik Schneider
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12925
UR - https://arxiv.org/abs/2609.12925
AB - We study the momentum equation of the decoupled unregularised Hibler sea-ice model with non-negative ice mass and ice strength, both of which may vanish. The ocean drag provides coercivity, while the stress law and mixed boundary conditions are encoded by a convex dissipation functional. We prove existence, uniqueness and stability for the time-discrete problem and reconstruct an admissible stress. A Rothe approximation yields global weak variational solutions for time-dependent coefficients under a one-sided growth condition on the mass. Weak solutions are unique when the ice strength is independent of time. For spatially Lipschitz ice strength, finite dissipation also yields a local measure structure of the weighted deformation and a global bound on the negative part of the weighted divergence.
ER -