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

Abstract

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 H3 type) for temperature than for velocity (of H2 type), using specifically the Neumann boundary condition for temperature. In fact, the case of Dirichlet condition for temperature remains as an open problem.