  We consider the inviscid generalized surface quasi-geostrophic equation
(gSQG) in a patch setting, where the parameter $\alpha \in (1,2)$. The cases
$\alpha = 0$ and $\alpha = 1$ correspond to 2d Euler and SQG respectively, and
our choice of the parameter $\alpha$ results in a velocity more singular than
in the SQG case.
  Our main result concerns the global stability of the half-plane patch
stationary solution, under small and localized perturbations. Our theorem
appears to be the first construction of stable global solutions for the
gSQG-patch equations. The only other nontrivial global solutions known so far
in the patch setting are the so-called V-states, which are uniformly rotating
and periodic in time solutions.
