  We analyze finite-time blowup scenarios of locally self-similar type for the
inviscid generalized surface quasi-geostrophic equation (gSQG) in
$\mathbb{R}^2$. Under an $L^r$ growth assumption on the self-similar profile
and its gradient, we identify appropriate ranges of the self-similar parameter
where the profile is either identically zero, and hence blowup cannot occur, or
its $L^p$ asymptotic behavior can be characterized, for suitable $r, p$.
Furthermore, we also generalize and improve on an analogous result proved in
[Xue; Journal of Differential Equations, 2016] concerning the SQG equation and
recover the results proved in [Cannone, Xue; Proceedings of the American
Mathematical Society, 2015] concerning the globally self-similar solutions of
the gSQG equation.
