Communications in Mathematical Sciences

Volume 16 (2018)

Number 7

The global attractor for the 3-D viscous primitive equations of large-scale moist atmosphere

Pages: 2003 – 2032

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n7.a11

Authors

Guoli Zhou (School of Statistics and Mathematics, Chongqing University, Chongqing, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Abstract

Absorbing ball in $H^1 (\mho)$ is obtained for the strong solution to the three dimensional viscous moist primitive equations under the natural assumption $Q_1, Q_2 \in L^2 (\mho)$ which is weaker than the assumption $Q_1, Q_2 \in H^1 (\mho)$ in the previous works. In view of the structure of the manifold and the special geometry involved with vertical velocity, the continuity of the strong solution in $H^1 (\mho)$ is established with respect to time and initial data. To obtain the existence of the global attractor for the moist primitive equations, the common method is to obtain the absorbing ball in $H^2 (\mho)$ for the strong solution to the equations. But it is difficult due to the complex structure of the moist primitive equations. To overcome the difficulty, we try to use Aubin–Lions lemma and the continuous property of the strong solutions to the moist primitive equations to prove the existence of the global attractor which improves the result obtained before, namely, the existence of weak attractor.

Keywords

moist primitive equations, uniform estimates, global attractor

2010 Mathematics Subject Classification

35Q35, 86A10

Full Text (PDF format)

Received 21 April 2018

Accepted 21 July 2018

Published 7 March 2019