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On the 3D viscous primitive equations of the large-scale atmosphere. (English) Zbl 1212.35348
Summary: This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in the paper by D. Huang and B. Guo [Sci. China, Ser. D 51, No. 3, 469–480 (2008)]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in $V$ for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of D. Huang and B. Guo (loc. cit.).
##### MSC:
 35Q30 Stokes and Navier-Stokes equations 65M70 Spectral, collocation and related methods (IVP of PDE) 86A10 Meteorology and atmospheric physics