Dynamics of the three dimensional viscous primitive equations of large-scale moist atmosphere

The objective of this paper is to study the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. Thanks to the presence of the strong coupling in the triple nonlinearity term and higher nonlinearity as well as the existence of corners of the domain under consideration, it is impossible to establish the existence of a more regular absorbing set. Therefore, it is very tricky to establish the existence of a global attractor in a more regular phase space. To overcome this difficulty, by obtaining the boundedness of the derivative of solutions in time, we prove the asymptotic compactness of the semigroup and establish the finite fractal dimension of the global attractor by using a smoothing property.

Keywords

global attractor, exponential attractor, primitive equations, smoothing property, asymptotic a priori estimate

2010 Mathematics Subject Classification

35B40, 35Q35, 37C60

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This work was supported by the National Science Foundation of China Grant (11401459, 11871389), the Natural Science Foundation of Shaanxi Province (2018JM1012) and the Fundamental Research Funds for the Central Universities (xjj2018088).

Received 18 November 2019

Accepted 1 March 2021

Published 2 August 2021