Geophysical Flow Models: An Approach by Quasilinear Evolution Equations

This thesis develops rigorous analysis of geophysical flow models in the context of Hibler's viscous-plastic sea ice model by means of quasilinear evolution equations. In a first step, well-posedness results for a fully parabolic variant are shown. Another focal point is the interaction problem of sea ice with a rigid body. Moreover, a coupled atmosphere-sea ice-ocean model is analyzed from a rigorous mathematical point of view. The first part of the thesis is completed by the local strong well-posedness of a parabolic-hyperbolic variant of Hibler's model. In the second part of the thesis, frameworks to quasilinear time periodic evolution equations are presented. One approach relies on maximal periodic regularity and the Arendt-Bu theorem, whereas the other one is based on the classical Da Prato-Grisvard theorem. Finally, applications of these frameworks to Hibler's sea ice model, Keller-Segel systems as well as a Nernst-Planck-Poisson type system are provided.