  We prove the persistence of boundary smoothness of vortex patches for
non-linear transport equations with velocity fields given by convolution of the
density with a kernel of the form $L(\nabla N),$ where $N$ is the fundamental
solution of the laplacian in $\mathbb{R}^n$ and $L$ a linear mapping of
$\mathbb{R}^n$ into itself. This allows the velocity field to have non-trivial
divergence. The quasi-geostrophic equation in $\mathbb{R}^3$ and the Cauchy
kernel in the plane are examples.
