Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability

Abstract

This article is devoted to the study of the asymptotic stability of the three-dimensional viscous primitive equations for large-scale moist atmosphere in the pressure coordinate system. An asymptotic stability criterion for the solutions of such model with time-dependent forcing terms is obtained. In particular, under the assumptions that the associated forces are both time-periodic and small (in a suitable sense), we obtain the existence of the time-periodic solution for the primitive equations of large-scale moist atmosphere. Moreover, this time-periodic solution is asymptotically stable in sense.

Keywords:

• primitive equations
• time-periodic solutions
• existence
• asymptotic stability

AMS Subject Classifications:

• 35
• 37
• 76
• 86

Notes

The first author was partially supported by the Ministry of Science and Technology, Taiwan under grant 102-2115-M-002-010-MY2. The second author was partially supported by the Ministry of Science and Technology, Taiwan under grant 102-2115-M-009-015-MY2.