Interaction of geophysical flows with sea ice dynamics

TL;DR

This paper proves well-posedness of a coupled ocean, atmosphere, and sea ice model using advanced mathematical techniques, including operator theory and quasilinear methods, to ensure stability near equilibrium states.

Contribution

It introduces a novel approach involving hydrostatic Dirichlet operators and investigates their properties, enabling the analysis of the coupled system's well-posedness.

Findings

Established local and global strong well-posedness near equilibria.

Developed a new method using hydrostatic Dirichlet-to-Neumann operators.

Proved the boundedness of the $ ext{H}^ ext{-}^ abla$-calculus for the linearized system.

Abstract

This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea ice model. In order to treat the coupling conditions, an approach involving the hydrostatic Dirichlet and Dirichlet-to-Neumann operator is developed. Mapping properties of the latter operators are investigated for the first time and are of central importance for showing that the operator associated with the linearized coupled system admits a bounded $\mathcal{H}^\infty$-calculus on suitable $\mathrm{L}^q$-spaces. Quasilinear methods allow then to obtain the strong well-posedeness results described above.