This article develops for the first time a rigorous analysis of Hibler’s model of sea ice dynamics. Identifying Hibler’s ice stress as a quasilinear second-order operator and regarding Hibler’s model as a quasilinear evolution equation, it is shown that a regularized version of Hibler’s coupled sea ice model, i.e., the model coupling velocity, thickness and compactness of sea ice, is locally strongly well-posed within the $$L_q$$ L q -setting and also globally strongly well-posed for initial data close to constant equilibria.

This article develops an approach to unique, strong periodic solutions to quasilinear evolution equations by means of the classical Da Prato-Grisvard theorem on maximal 𝐿 𝑝 -regularity in real interpolation spaces. The method is used to show that quasilinear Keller-Segel systems admit a unique, strong 𝑇-periodic solution in a neighborhood of 0 provided the external forces are 𝑇-periodic and satisfy certain smallness conditions. A similar assertion applies to a Nernst-Planck-Poisson type system in electrochemistry. The proof for the quasilinear Keller-Segel systems relies also on a new mixed derivative theorem in real interpolation spaces, that is, Besov spaces, which is of independent interest.