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In this paper for either the sharp front Surface Quasi-Geostrophic equationor the Muskat problem we rule out the "splash singularity" blow-up scenario; inother words we prove that the contours evolving from either of these systemscan not intersect at a single point while the free boundary remains smooth.Splash singularities have been shown to hold for the free boundaryincompressible Euler equation in the form of the water waves contour evolutionproblem \cite{ADCPJ}. Our result confirms the numerical simulations in\cite{CFMR} where it is shown that the curvature blows up due to the contourscollapsing at a point. Here we prove that maintaining control of the curvaturewill remove the possibility of pointwise interphase collapse. Anotherconclusion that we provide is a better understanding of the work \cite{DP3} inwhich squirt singularities are ruled out; here a positive volume of fluidbetween the contours can not be ejected in finite time.

Absence of splash singularities for SQG sharp fronts and the Muskat problem