On the quasi-geostrophic equations on compact closed surfaces in R3

The quasi-geostrophic equations on compact surfaces in R3 without boundary are studied by means of the theory of quasi-linear parabolic evolution equations based on maximal Lp-regularity. It is shown that the problem is globally strongly well-posed in Lq, the solutions regularize instantly and form a global semiflow in the proper state manifold, and, as time goes to infinity, a solution converges exponentially to a constant in the topology of the state space.