28 citations · 62 across the 7 of their papers we have counts for
9 papers
Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
Francisco Gancedo, Rafael Granero-Belinchon, Stefano Scrobogna
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayle…
Well-posedness of a water wave model with viscous effects
Rafael Granero-Belinchón, Stefano Scrobogna
Starting from the paper by Dias, Dyachenko and Zakharov (\emph{Physics Letters A, 2008}) on viscous water waves, we derive a model that describes water waves with viscosity moving…
Rigorous Asymptotic Models of Water Waves
C. H. Arthur Cheng, Rafael Granero-Belinchon, Steve Shkoller +1
We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interacti…
On the local and global existence of solutions to 1D transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &θ_t+uθ_x+νΛ^γθ=0, \\ & u=\mathcal{N}(θ), \end{split} \end{equat…
On the thin film Muskat and the thin film Stokes equations
Gabriele Bruell, Rafael Granero-Belinchón
The present paper is concerned with the analysis of two strongly coupled systems of degenerate parabolic partial differential equations arising in multiphase thin film flows. In pa…
A model for Rayleigh-Taylor mixing and interface turn-over
Rafael Granero-Belinchón, Steve Shkoller
We first develop a new mathematical model for two-fluid interface motion, subjected to the Rayleigh-Taylor (RT) instability in two-dimensional fluid flow, which in its simplest for…
On a drift-diffusion system for semiconductor devices
Rafael Granero-Belinchón
In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two a…
Local solvability and turning for the inhomogeneous Muskat problem
Luigi Berselli, Diego Cordoba, Rafael Granero-Belinchon
In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can f…
Global existence for the confined Muskat problem
Rafael Granero-Belinchón
In this paper we show global existence of Lipschitz continuous solution for the stable Muskat problem with finite depth (confined) and initial data satisfying some smallness condit…