Abstract
In this paper, we investigate a generalized two-component rotational b-family system arising in the rotating fluid with the effect of the Coriolis force. First, we study the persistence properties of the system in weighted \begin{document}$ L^p $\end{document} -spaces, for a large class of moderate weights. Secondly, in order to overcome the difficulty arising from higher order nonlinearity and no conservation law, we take the advantage of the specially intrinsic structure of the system and make use of commutator estimate, and then derive two blow-up results for the strong solutions to the system.
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