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By studying the linearization of contour dynamics equation and using implicitfunction theorem, we prove the existence of co-rotating and travelling globalsolutions for the gSQG equation, which extends the result of Hmidi and Mateu\cite{HM} to $\alpha\in[1,2)$. Moreover, we prove the $C^\infty$ regularity ofvortices boundary, and show the convexity of each vortices component.

Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation