9 papers · 1 filter
Finite time singularity formation for a nonlocal Boussinesq system arising in cold-plasma dynamics
Diego Alonso-Orán, Rafael Granero-Belinchón
We study finite-time singularity formation for a nonlocal Boussinesq system arising in cold-plasma dynamics. We show that smooth, symmetric initial data with strictly positive tota…
Pseudo-differential noise and nonlocal singularity formation in the stochastic Córdoba--Córdoba--Fontelos equation
Diego Alonso-Orán, Rafael Granero-Belinchón, Yingting Miao +1
We study the stochastic Córdoba--Córdoba--Fontelos equation driven by multiplicative Stratonovich noise. The noise amplitude is allowed to be a pseudo-differential operator whose l…
Asymptotic models for viscoelastic one-dimensional blood flow
Diego Alonso-Orán, Rafael Granero-Belinchón, Carlos Yanes Pérez
We derive a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries. We prove local well-posedness of strong solutions in Sobolev spaces for general…
Weakly nonlinear models for hydroelastic water waves
Diego Alonso-Orán, Rafael Granero-Belinchón, Juliana S. Ziebell
In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidi…
A bifurcation theory approach to the nonlocal Kuramoto-Sivashinsky equation
Pablo Cubillos, Rafael Granero-Belinchón, Juan Carlos Sampedro
We study the nonlocal Kuramoto-Sivashinsky equation on the one-dimensional torus, \[ u_t+u u_x=Λ^{r}u-\varepsilon Λ^{s}u,\qquad x\in\mathbb T, \] where , , $r\i…
A fluid-solid interaction problem in porous media
Diego Alonso-Orán, Rafael Granero-Belinchón
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of s…
Unstable Interface Dynamics for Gravity Stokes Flow
Francisco Gancedo, Rafael Granero-Belinchón, Zhongtian Hu +2
We investigate some unstable behavior of the interface given by two incompressible fluids of different densities evolving by the regular Stokes law with gravity force. In the unsta…
A new asymptotic model of multilayer tumor growth
Rafael Granero-Belinchón, Martina Magliocca
In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance,…
Asymptotic models for the evolution of a circular biofilm
Diego Alonso-Orán, Ana Carpio, Rafael Granero-Belinchón
We study a class of lubrication-type equations modeling the spread of thin poroelastic biofilms at air/agar interfaces. Starting from a biofilm slab model, we perform a formal mult…