47 citations · 265 across the 22 of their papers we have counts for
6 papers · 1 filter
Well-posedness of the Muskat problem with initial data
C. H. Arthur Cheng, Rafael Granero-Belinchón, Steve Shkoller
We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat…
Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux
Jan Burczak, Rafael Granero-Belinchón
A semilinear version of parabolic-elliptic Keller-Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutio…
Global existence for some transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one dimensional model of…
On the effect of boundaries in two-phase porous flow
Rafael Granero-Belinchón, Gustavo Navarro, Alejandro Ortega
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its…
On a nonlocal analog of the Kuramoto-Sivashinsky equation
Rafael Granero-Belinchón, John K. Hunter
We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to…
On a generalized doubly parabolic Keller-Segel system in one spatial dimension
Jan Burczak, Rafael Granero-Belinchón
We study a doubly parabolic Keller-Segel system in one spatial dimension, with diffusions given by fractional laplacians. We obtain several local and global well-posedness results…