4 citations · 10 across the 7 of their papers we have counts for
7 papers · 1 filter
Global well-posedness of critical surface quasigeostrophic equation on the sphere
Diego Alonso-Oran, Antonio Cordoba, Angel D. Martinez
In this paper we prove global well-posedness of the critical surface quasigeostrophic equation on the two dimensional sphere building on some earlier work of the authors. The proof…
Continuity of weak solutions of the critical quasigeostrophic equation on the sphere
Diego Alonso-Oran, Antonio Cordoba, Angel D. Martinez
In this paper we provide regularity results for active scalars that are weak solutions of almost critical drift-diffusion equations in general surfaces. This includes models of ani…
A pointwise inequality for fractional laplacians
Antonio Cordoba, Angel D. Martinez
The fractional laplacian is an operator appearing in several evolution models where diffusion coming from a Lévy process is present but also in the analysis of fluid interphases. W…
Porous media: the Muskat problem in 3D
Antonio Cordoba, Diego Cordoba, Francisco Gancedo
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the Rayleigh-Taylor condition…
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…