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arxiv: 2604.26295 · v1 · submitted 2026-04-29 · 🧮 math.AP · physics.ao-ph· physics.geo-ph

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A mathematical study of an elastic-viscous-plastic sea-ice model with the Kelvin-Voigt rheology

Daniel W. Boutros , Xin Liu , Marita Thomas , Edriss S. Titi
Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:17 UTC · model grok-4.3

classification 🧮 math.AP physics.ao-phphysics.geo-ph
keywords elastic-viscous-plastic sea-ice modelKelvin-Voigt rheologywell-posednessstress tensor estimateadvection termviscosity regularizationnon-Newtonian fluid
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The pith

Introducing Kelvin-Voigt viscosity into the momentum balance of an elastic-viscous-plastic sea-ice model yields local well-posedness with advection and global well-posedness without it through a new stress tensor bound.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors study a version of the elastic-viscous-plastic sea-ice model that incorporates Kelvin-Voigt rheology directly in the momentum equation. They establish local-in-time existence and uniqueness of solutions when the advection term is present and global existence when it is omitted. The key technical step is deriving a new supremum bound on the stress tensor that exploits the damping provided by the viscosity term. This approach succeeds without imposing an artificial upper limit on the viscosity coefficients and works for initial conditions that are less smooth than those required in related prior results. Such mathematical guarantees are relevant because these models underpin large-scale simulations of sea ice in climate studies.

Core claim

We formulate an elastic-viscous-plastic sea-ice model with Kelvin-Voigt regularisation in the momentum balance and prove the local well-posedness for the model with the advection term and the global well-posedness in the absence of the advection term. A crucial component of the proof is a new L^∞-estimate for the stress tensor which relies on the damping structure. We handle viscosity coefficients without a cutoff from above and prove existence for much less regular initial data.

What carries the argument

The damping structure provided by the Kelvin-Voigt term in the momentum balance, enabling the L^∞ estimate for the stress tensor.

If this is right

  • Solutions exist locally in time even when the full advection term is retained in the momentum equation.
  • Global-in-time solutions exist when the advection term is omitted from the momentum balance.
  • Well-posedness holds for viscosity coefficients that lack any artificial upper bound.
  • Existence results apply to initial data of lower regularity than those treated in the authors' prior Voigt-EVP work.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The damping-derived stress bound may transfer to other non-Newtonian fluid systems that combine elastic and viscous effects.
  • Numerical climate codes could adopt this regularization to bypass cutoff restrictions that currently limit fidelity.
  • Long-time stability or attractor properties of the solutions remain open for further analysis.

Load-bearing premise

The Kelvin-Voigt damping term in the momentum balance produces a uniform L^∞ bound on the stress tensor under the given model assumptions.

What would settle it

A concrete initial datum for which the stress tensor norm becomes unbounded in finite time despite the damping term, or for which no solution exists even locally.

read the original abstract

Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations, we proposed in [D. W. Boutros, X. Liu, M. Thomas and E. S. Titi, arXiv:2505.03080 (2025)] the use of the inviscid Voigt regularisation for the constitutive (stress-tensor) relation and proved the global well-posedness of the resulting model. The EVP model treats sea ice as a non-Newtonian fluid. In turn, elastic-viscous-plastic solids often involve a Kelvin-Voigt viscosity in terms of the strain rate. Therefore, in the present work we formulate an elastic-viscous-plastic sea-ice model with a Kelvin-Voigt regularisation in terms of the strain rate. In other words, we introduce the Voigt regularisation in the momentum balance rather than in the constitutive relation (for the stress tensor). We then prove the local well-posedness for the Kelvin-Voigt EVP model with the advection term, in the momentum balance, and the global well-posedness in the absence of the advection term (following a very standard approximation in the latter case). A crucial component of the proof of these results, is a new $L^\infty$-estimate for the stress tensor which relies on the damping structure. Note that, both with and without the advection term, we are able to handle the case of viscosity coefficients without a cutoff from above, which remains a major open problem for the closely related Hibler sea-ice model. We are also able to prove the existence of solutions for much less regular initial data compared to our previous paper on the Voigt-EVP model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper formulates an elastic-viscous-plastic sea-ice model with Kelvin-Voigt regularization placed in the momentum balance (rather than the constitutive relation) and proves local well-posedness of the system including the advection term together with global well-posedness when advection is omitted. Both results rest on a new L^∞ estimate for the stress tensor that exploits the damping structure of the Kelvin-Voigt term; the analysis accommodates viscosity coefficients without an upper cutoff and initial data of lower regularity than in the authors' prior Voigt-EVP work.

Significance. If the claimed L^∞ bound on the stress tensor is valid, the results constitute a concrete advance for the mathematical theory of sea-ice models used in climate simulations. They remove the artificial upper cutoff on viscosity coefficients that remains open for the related Hibler model and lower the regularity threshold on initial data, while the global existence result without advection follows standard approximation techniques.

major comments (1)
  1. [Proof of the a priori L^∞ estimate for the stress tensor (in the section containing the energy estimates and maximum-prc] The new L^∞ estimate for the stress tensor (central to both Theorem statements on local and global well-posedness) must be shown to control the nonlinear plastic contribution and any transport effects while using only the given constitutive law and the Kelvin-Voigt damping term. The derivation should explicitly confirm that no implicit upper bound on the viscosity coefficients or extra regularity on the data is required, as this is the load-bearing step for the main claims.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from an explicit statement of the precise function spaces in which local and global solutions are obtained.
  2. [Introduction] A short comparison table or paragraph contrasting the regularity assumptions here with those in the authors' previous Voigt-EVP paper (arXiv:2505.03080) would clarify the improvement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our paper. We are pleased that the significance of the results is recognized. Below we provide a point-by-point response to the major comment.

read point-by-point responses

  1. Referee: [Proof of the a priori L^∞ estimate for the stress tensor (in the section containing the energy estimates and maximum-prc] The new L^∞ estimate for the stress tensor (central to both Theorem statements on local and global well-posedness) must be shown to control the nonlinear plastic contribution and any transport effects while using only the given constitutive law and the Kelvin-Voigt damping term. The derivation should explicitly confirm that no implicit upper bound on the viscosity coefficients or extra regularity on the data is required, as this is the load-bearing step for the main claims.

    Authors: We appreciate the referee's emphasis on the importance of this estimate. The L^∞ bound is derived in the energy estimates section by testing the constitutive relation with the stress tensor itself, leveraging the positive damping term from the Kelvin-Voigt regularization in the momentum equation to control the growth. This approach directly handles the nonlinear plastic term through the structure of the model and accounts for transport effects via integration by parts or commutator estimates that do not require additional regularity. The derivation relies solely on the constitutive law and the damping, without any upper bound on the viscosity coefficients (which is a key feature distinguishing our result from the Hibler model) and with the initial data regularity as stated in the theorems. To address the referee's request for explicit confirmation, we will revise the manuscript by adding a remark immediately following the estimate that summarizes these properties and verifies the absence of implicit assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity: direct PDE existence proof via a priori estimates

full rationale

The paper establishes local well-posedness (with advection) and global well-posedness (without advection) for the Kelvin-Voigt EVP sea-ice model through standard mathematical techniques: derivation of a new L^∞ bound on the stress tensor from the damping term in the momentum equation, followed by approximation arguments and energy estimates. This chain relies on the constitutive law and the Kelvin-Voigt regularization without any reduction to fitted parameters, self-definitional loops, or load-bearing self-citations. The cited prior work (arXiv:2505.03080) supplies only motivational context for the model choice and is not invoked to justify the current estimates or uniqueness. The derivation is self-contained against external PDE benchmarks and does not rename known results or smuggle ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard EVP sea-ice equations plus the added Kelvin-Voigt damping term in momentum balance, together with classical PDE theory for existence; no free parameters or new physical entities are introduced.

axioms (2)
  • domain assumption The sea-ice dynamics follow the standard elastic-viscous-plastic constitutive framework with the Kelvin-Voigt term inserted into the momentum equation.
    The model is constructed by modifying the established EVP equations as described in the abstract.
  • standard math Standard assumptions on the spatial domain, boundary conditions, and Sobolev-type function spaces hold for the well-posedness analysis.
    Implicit in any local/global existence proof for evolutionary PDE systems.

pith-pipeline@v0.9.0 · 5679 in / 1504 out tokens · 115690 ms · 2026-05-07T13:17:08.354816+00:00 · methodology

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Reference graph

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