Well-posedness of a coupled atmosphere-sea ice-ocean model ...

• Main Authors: Binz, Tim, Brandt, Felix, Hieber, Matthias
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2022
• Subjects: Analysis of PDEs math.AP; FOS Mathematics; 35Q86, 35K59, 86A05, 86A10, 35Q35; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.2209.13150; https://arxiv.org/abs/2209.13150

This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of the ocean and the atmosphere with a regularized version of Hibler's viscous-plastic sea ice model. Following the situation of the plane Couette flow, the ocean force on the sea ice is proportional to the shear rate and the velocity of the ocean and the ice coincide on their common interface. In addition, it is assumed that the atmosphere exerts a force on the sea ice via atmospheric winds. To deal with the coupled system, we consider the stationary hydrostatic Stokes problem and study the associated Dirichlet and Dirichlet-to-Neumann operator. The latter operators are of independent interest. Our strategy is to include the interface condition into the domain of the associated operator, which, however, then has non-diagonal domain. A new decoupling approach using the above hydrostatic Dirichlet and Dirichlet-to-Neumann operator is presented. ...