3 citations · 3 across the 3 of their papers we have counts for
3 papers · 1 filter
Interface evolution: water waves in 2-D
Antonio Cordoba, Diego Cordoba, Francisco Gancedo
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, i…
Interface evolution: the Hele-Shaw and Muskat problems
Antonio Cordoba, Diego Cordoba, Francisco Gancedo
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy's law. The free boundary is given by the discontinui…
Formation of singularities for a transport equation with nonlocal velocity
Antonio Cordoba, Diego Cordoba, Marco A. Fontelos
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the…