Local null controllability of the complete N-dimensional Ladyzhenskaya-Boussinesq model

This work investigates both local null controllability and large time null controllability for a class of complete Ladyzhenskaya Boussinesq systems, where the controls are distributed and supported on small subsets of the domain. The proof of local null controllability relies on classical techniques, including Carleman estimates and Liusternik Inverse Mapping Theorem. Nevertheless, the presence of nonlinearities in both the velocity and temperature equations necessitates careful treatment.