On the quasi-geostrophic equations on compact closed surfaces in
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文摘
The quasi-geostrophic equations on compact surfaces in R3R3 without boundary are studied by means of the theory of quasi-linear parabolic evolution equations based on maximal LpLp-regularity. It is shown that the problem is globally strongly well-posed in LqLq, 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.