Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2511.09327

On the Singular Limit in Hibler's Sea Ice Model

Robert Denk·Franz Gmeineder·Matthias Hieber
View original source ↗Read source document ↗Export metadata ↓

Abstract

We establish the existence of energy-driven solutions to the momentum balance equation in Hibler's sea ice model. As a main novelty and different from previous results, we deal with the singular limit and therefore cover the true unregularized Hibler stress. To this end, we introduce an energy-based notion of solution that is able to capture plasticity effects of sea ice. This requires certain relaxations of the Hibler energies and, by the different function space set-up, comes with novel challenges. In particular, we establish a bulk approximation result of the boundary terms in the evolutionary relaxed Hibler energies. This is achieved by developing a novel reduction scheme for nonlinear trace expressions which should be of independent interest. Finally, based on our main results, we classify our findings within a broader concept of solutions that is applicable to the non-constant mass case too.

Explore related subjects

math.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Robert Denk, Franz Gmeineder, Matthias Hieber. 2025-11-12. On the Singular Limit in Hibler's Sea Ice Model. https://arxiv.org/abs/2511.09327

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A linear test approach to global controllability of third- and fifth-order nonlinear dispersive equations

We investigate third- and fifth-order nonlinear dispersive equations of KdV type on the torus and establishes approximate controllability by a fixed four-dimensional control; rather than relying solely on the saturation machinery, the analysis exploits the finite-dimensional controllability of the inviscid Burgers equation linearized around a carefully constructed return trajectory, with the trajectory itself obtained from an observable family. This ``linear test" strategy, yields more information about the structure of the control than the standard approach. In particular, the constructed control is shown to depend continuously on the initial and target states, a property that is by no means automatic in nonlinear control problems, and to decompose as a bounded linear operator applied to the data plus a fixed remainder, with the operator part interestingly independent of the order of dispersion.

math.AP↗
arXiv2026

A conditional Lagrangian clock barrier at the $C^{1,\frac{1}{3}}$ threshold for axisymmetric Euler without swirl

We consider axisymmetric no-swirl solutions to the three-dimensional incompressible Euler equations, with initial velocity in $C^{1,α}\cap L^2$, where $α\in\left[\frac{1}{3},1\right)$. In a major breakthrough, Shkoller introduced a clock-and-driver framework that he used in order to prove finite-time type I blow-up below the $C^{1,\frac{1}{3}}$ threshold in this setting. Motivated by this, we define Lagrangian classes of coherent conditional solutions for which the same mechanism yields a supercritical-critical barrier to blow-up when $α\geq\frac{1}{3}$. When $α>\frac{1}{3}$, the aforementioned barrier is genuinely depleted, whereas at the critical endpoint $α=\frac{1}{3}$, we obtain an exponential bound preventing blow-up. In the general case, we formulate a matrix-clock criterion in terms of the smallest singular value of the deformation gradient and show that, under transverse cusp-tail, longitudinal, off-clock, Dini, and suitable geometric coherence hypotheses, this singular value cannot collapse in finite time. In particular, we also show that the class of such coherent solutions includes the smooth ones locally in time. In the on-axis case, the criterion reduces to the scalar clock inequality $\displaystyle \dot{J}(t)\gtrsim -B(t)J(t)-CJ(t)^{3α}$, which rules out Shkoller-type clock collapse for $α\geq\frac{1}{3}$. These results do not enlarge the known Lorentz-space global regularity classes. Rather, they in particular identify the supercritical Lagrangian obstruction dual to Shkoller's subcritical blow-up mechanism in the case $α>\frac{1}{3}$.

math.AP↗