On Nonexistence of Splash Singularities for the α -SQG Patches


Kiselev, A; Luo, X


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.


Kiselev, A., and X. Luo. “On Nonexistence of Splash Singularities for the α -SQG Patches.” Journal of Nonlinear Science 33, no. 2 (April 1, 2023). https://doi.org/10.1007/s00332-023-09893-2.
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