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Global attractors for the three-dimensional viscous primitive equations of large-scale atmosphere in log-pressure coordinate. (English) Zbl 1291.86009

Summary: We first prove the existence of \((V, V)\)- and \((V, H^2)\)-absorbing sets for the three-dimensional primitive equations of large-scale atmosphere in log-pressure coordinate and then prove the existence of \((V, H^3)\)-absorbing set by the use of the elliptic regularity theory. Finally, we obtain the existence of \((V, V)\)- and \((V, H^2)\)-global attractors for the three-dimensional viscous primitive equations of large-scale atmosphere in log-pressure coordinate by using the Sobolev compactness embedding theory.

MSC:

86A10 Meteorology and atmospheric physics
35B41 Attractors
35Q35 PDEs in connection with fluid mechanics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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