32 citations · 60 across the 6 of their papers we have counts for
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Derivation and well-posedness for asymptotic models of cold plasmas
Diego Alonso-Orán, Ángel Durán, Rafael Granero-Belinchón
In this paper we derive three new asymptotic models for an hyperbolic-hyperbolicelliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The fi…
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…
Asymptotic shallow models arising in magnetohydrodynamics
Diego Alonso-Orán
In this paper, we derive a new shallow asymptotic model for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equation, vital in describing large-scale pr…
The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions
Diego Alonso-Orán, Aythami Bethencourt de León, So Takao
In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation a…
On the well-posedness of stochastic Boussinesq equations with cylindrical multiplicative noise
Diego Alonso-Orán, Aythami Bethencourt de León
The Boussinesq equations are fundamental in meteorology. Among other aspects, they aim to model the process of front formation. We use the approach presented in [Hol15] to introduc…
Stability, well-posedness and blow-up criterion for the Incompressible Slice Model
Diego Alonso-Orán, Aythami Bethencourt de León
In atmospheric science, slice models are frequently used to study the behaviour of weather, and specifically the formation of atmospheric fronts, whose prediction is fundamental in…