Time-periodic solutions for a generalized Boussinesq model with Neumann boundary conditions for temperature

The aim of this work is to prove the existence of regular time-periodic solutions for a generalized Boussinesq model (with nonlinear diffusion for the equations of velocity and temperature). The main idea is to obtain higher regularity (of H 3 type) for temperature than for velocity (of H 2 type), using specifically the Neumann boundary condition for temperature. In fact, the case of Dirichlet condition for temperature remains as an open problem.