47 citations · 265 across the 22 of their papers we have counts for
33 papers · 1 filter
Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data
Diego Alonso-Orán, Rafael Granero-Belinchón
In this work we study the inhomogeneous Muskat problem, \emph{i.e.} the evolution of an internal wave between two different fluids in a porous medium with discontinuous permeabilit…
On the motion of gravity-capillary waves with odd viscosity
Rafael Granero-Belinchón, Alejandro Ortega
We develop three asymptotic models of surface waves in a non-newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applicati…
Global well-posedness and decay for viscous water wave models
Rafael Granero-Belinchón, Stefano Scrobogna
The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical a…
Global existence in the Lipschitz class for the N-Peskin problem
Francisco Gancedo, Rafael Granero-Belinchón, Stefano Scrobogna
In this paper we study a toy model of the Peskin problem that captures the motion of the full Peskin problem in the normal direction and discards the tangential elastic stretching…
Well-posedness of the water-wave with viscosity problem
Rafael Granero-Belinchón, Stefano Scrobogna
In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability i…
Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems
Hantaek Bae, Rafael Granero-Belinchón
In this work we prove that the solution of the Serre-Green-Naghdi equation cannot be globally defined when the interface reaches the impervious bottom tangentially. As a consequenc…
On a thin film model with insoluble surfactant
Gabriele Bruell, Rafael Granero-Belinchón
This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary…
On the dynamics of 3D electrified falling films
Jiao He, Rafael Granero-Belinchón
In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing the global wellposedness of this equation…
Models for damped water waves
Rafael Granero-Belinchón, Stefano Scrobogna
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take int…
Growth in the Muskat problem
Rafael Granero-Belinchón, Omar Lazar
We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initia…
On a nonlocal differential equation describing roots of polynomials under differentiation
Rafael Granero-Belinchón
In this work we study the nonlocal transport equation derived recently by Steinerberger when studying how the distribution of roots of a polynomial behaves under iterated different…
On an asymptotic model for free boundary Darcy flow in porous media
Rafael Granero-Belinchón, Stefano Scrobogna
We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove…
Asymptotic models for free boundary flow in porous media
Rafael Granero-Belinchón, Stefano Scrobogna
We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness par…
Global existence and decay to equilibrium for some crystal surface models
Rafael Granero-Belinchón, Martina Magliocca
In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations Thes…
Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations
Jan Burczak, Rafael Granero-Belinchón
In this paper we consider a -dimensional () parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order . We prove un…
Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability
Rafael Granero-Belinchón, Steve Shkoller
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is de…
Suppression of blow up by a logistic source in D Keller-Segel system with fractional dissipation
Jan Burczak, Rafael Granero-Belinchón
We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order . We obtain existence of global in time regula…
Global existence of weak solutions to dissipative transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider 1D dissipative transport equations with nonlocal velocity field: \[ θ_t+uθ_x+δu_{x} θ+Λ^γθ=0, \quad u=\mathcal{N}(θ), \] where is a nonlocal operator give…
Global solutions for a hyperbolic-parabolic system of chemotaxis
Rafael Granero-Belinchón
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
On the fractional Fisher information with applications to a hyperbolic-parabolic system of chemotaxis
Rafael Granero-Belinchón
We introduce new lower bounds for the fractional Fisher information. Equipped with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove the global existence o…
On the generalized Buckley-Leverett equation
Jan Burczak, Rafael Granero-Belinchón, Garving K. Luli
In this paper we study the generalized Buckley-Leverett equation with nonlocal regularizing terms. One of these regularizing terms is diffusive, while the other one is conservative…
Global solutions for a supercritical drift-diffusion equation
Jan Burczak, Rafael Granero-Belinchón
We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation…
Critical Keller-Segel meets Burgers on : large-time smooth solutions
Jan Burczak, Rafael Granero-Belinchón
We show that solutions to the parabolic-elliptic Keller-Segel system on with critical fractional diffusion remain smooth for any initial data and…
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…