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The status of disturbances of both initial values and parameters in the model is further investigated, and the exact explicit estimates on the disturbance energy and disturbance potential enstrophy are given, while the initial disturbance fields depend only on the initial disturbance potential enstrophy, initial disturbance velocity circulation along the boundary, and disturbance parameters. And based on the generalized nonlinear stability concept in the sense of Lyapunov, the nonlinear stability criteria paralleling to Arnold’s second theorem are obtained.
The status of disturbances of both initial values and parameters in the model is further investigated, and the exact explicit estimates on the disturbance energy and disturbance potential enstrophy are given, while the initial disturbance fields depend on the initial disturbance potential enstrophy, initial disturbance velocity velocity And based on the generalized nonlinear stability concept in the sense of Lyapunov, the nonlinear stability criteria paralleling to Arnold’s second theorem are obtained.