Regular Time-Reproductive Solutions for Generalized Boussinesq Model with Neumann Boundary Conditions for Temperature

The aim of this work is to prove existence of regular time reproductive solutions for a generalized Boussinesq model (with nonlinear diffusion for 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.