68 citations · 100 across the 11 of their papers we have counts for
16 papers
Local wellposedness for the free boundary incompressible Euler equations with interfaces that exhibit cusps and corners of nonconstant angle
Diego Córdoba, Alberto Enciso, Nastasia Grubic
We prove that free boundary incompressible Euler equations are locally well posed in a class of solutions in which the interfaces can exhibit corners and cusps. Contrary to what ha…
Non existence and strong ill-posedness in and Sobolev spaces for SQG
Diego Córdoba, Luis Martínez-Zoroa
We construct solutions in with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in () but that are not in for…
Existence of gravity-capillary Crapper waves with concentrated vorticity
Diego Córdoba, Elena Di Iorio
The aim of this paper is to prove the existence of gravity-capillary Crapper waves with the presence of vorticity. In particular, we consider a concentrated vorticity: point vortex…
Stability of traveling waves for the Burgers-Hilbert equation
Ángel Castro, Diego Córdoba, Fan Zheng
We consider smooth solutions of the Burgers-Hilbert equation that are a small perturbation from a global periodic traveling wave with small amplitude . We use a modified ene…
The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation
Ángel Castro, Diego Córdoba, Fan Zheng
We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation from a radial stationary solution . We use a modified en…
On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term
Angel Castro, Diego Córdoba, Daniel Lear
We consider the 2D Boussinesq equations with a velocity damping term in a strip , with impermeable walls. In this physical scenario, where the \textit{Bouss…
Uniqueness for SQG patch solutions
Antonio Córdoba, Diego Córdoba, Francisco Gancedo
This paper is about the evolution of a temperature front governed by the Surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces w…
Global smooth solutions for the inviscid SQG equation
Angel Castro, Diego Córdoba, Javier Gómez-Serrano
In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
On the existence of stationary splash singularities for the Euler equations
Diego Córdoba, Alberto Enciso, Nastasia Grubic
In this paper we discuss the existence of stationary incompressible fluids with splash singularities. Specifically, we show that there are stationary solutions to the Euler equatio…
Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations
Angel Castro, Diego Córdoba, Javier Gómez-Serrano
Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we…
Non-splat singularity for the one-phase Muskat problem
Diego Córdoba, Tania Pernas-Castaño
For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is…
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 water waves with surface tension
Angel Castro, Diego Córdoba, Charles Fefferman +2
Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singulari…
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…
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…