139 citations · 833 across the 40 of their papers we have counts for
4 papers · 2 filters
Finite time singularities for the free boundary incompressible Euler equations
Angel Castro, Diego Córdoba, Charles Fefferman +2
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave pro…
Splash singularity for water waves
Angel Castro, Diego Córdoba, Charles Fefferman +2
We exhibit smooth initial data for the 2D water wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result t…
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
Angel Castro, Diego Cordoba, Charles Fefferman +2
The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of th…
Generalized surface quasi-geostrophic equations with singular velocities
Dongho Chae, Peter Constantin, Diego Córdoba +2
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular int…