On Nonexistence of Splash Singularities for the α -SQG Patches

In this paper, we consider patch solutions to the α-SQG equation and derive new criteria for the absence of splash singularity where different patches or parts of the same patch collide in finite time. Our criterion refines a result due to Gancedo and Strain Gancedo and Strain (2014), providing a condition on the growth of curvature of the patch necessary for the splash and an exponential in time lower bound on the distance between patches with bounded curvature.