Global well-posedness for a rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number

We analyze a three-dimensional rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number, i.e., when the momentum diffusivity is much more dominant than the thermal diffusivity. Consequently, the dynamics of the velocity field takes place at a much faster time scale than the temperature fluctuation, and at the limit the velocity field formally adjusts instantaneously to the thermal fluctuation. We prove the global well-posedness of weak solutions and strong solutions to this model.

Automated summary

In this model, the dynamics of the velocity field occur at a much faster time scale than the temperature fluctuation, and the velocity field formally adjusts instantaneously to the thermal fluctuation at the limit. The global well-posedness of weak solutions and strong solutions to this model has been proven.