Heat transport in rotating convection

We derive upper bounds for the Nusselt number in infinite Prandtl number rotating convection. The bounds decay alge-braically with Taylor number to the conductive heat transport value; the decay rate depends on boundary conditions. We show moreover that when the rotation is fast enough the purely conductive solution is the globally and nonlinearly attractive fixed point; the critical rotation rate also depends on boundary conditions. The influence of the boundary conditions is explained physically in terms of Ekman layers.