In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the "splash singularity" blow-up scenario; in other words, we prove that the contours evolving from either of these systems cannot intersect at a single point while the free boundary remains smooth. Splash singularities have been shown to hold for the free boundary incompressible Euler...

We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization scheme à la [R. Jordan, D. Kinderlehrer & F. Otto, SIAM J. Math. Anal, 2...

sedimentation in reservoirs reduces dams storage and makes many problems in their operation. therefore accurate computation of sediment volume is essential for appropriate design and optimum reservoir management during its operation. in this research long term field data of sefid-rood dam were used to check the sediment volume computed for ghezelozan basin. the computed volume of sediment by ra...