4 papers
Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity
Angel Castro, David Lannes
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case…
Structural stability for the splash singularities of the water waves problem
Angel Castro, Diego Córdoba, Charles Fefferman +2
In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a g…
Remarks on geometric properties of SQG sharp fronts and -patches
Angel Castro, Diego Córdoba, Javier Gómez-Serrano +1
Guided by numerical simulations, we present the proof of two results concerning the behaviour of SQG sharp fronts and -patches. We establish that ellipses are not rotational sol…
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…