2 citations · 4 across the 11 of their papers we have counts for
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Remarks on some quasi-linear fourth order parabolic equations arising in mathematical physics
Francesco Fanelli, Rafael Granero-Belinchón, Martina Magliocca +1
This note proves existence and uniqueness of strong solutions to a broad class of fourth-order quasi-linear parabolic equations in the class of Wiener spaces. It improves upon prev…
New functional inequalities with applications to the arctan-fast diffusion equation
Rafael Granero-Belinchón, Martina Magliocca, Alejandro Ortega
In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads $…
On the global well-posedness of interface dynamics for gravity Stokes flow
Francisco Gancedo, Rafael Granero-Belinchón, Elena Salguero
In this paper we establish the global-in-time well-posedness for an arbitrary , , initial internal wave for the free boundary gravity Stokes system in two dimension…
Well-posedness and decay for a nonlinear propagation wave model in atmospheric flows
Diego Alonso-Orán, Rafael Granero-Belinchón
In this note, we provide two results concerning the global well-posedness and decay of solutions to an asymptotic model describing the nonlinear wave propagation in the troposphere…
Global existence for certain fourth order evolution equations
Rafael Granero-Belinchón, Martina Magliocca
In this paper we establish three global in time results for two fourth order nonlinear parabolic equations. The first of such equations involves the Hessian and appears in epitaxia…
A nonlocal equation describing tumor growth
Rafael Granero-Belinchón, Martina Magliocca
Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony…
Well-posedness for an hyperbolic-hyperbolic-elliptic system describing cold plasmas
Diego Alonso-Orán, Rafael Granero-Belinchón
In this short note, we provide the well-posedness for an hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of collision free-plasma in magnetic fields. The proof…
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…
Long time interface dynamics for gravity Stokes flow
Francisco Gancedo, Rafael Granero-Belinchón, Elena Salguero
We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravi…
Well-posedness theory for non-homogeneous incompressible fluids with odd viscosity
Francesco Fanelli, Rafael Granero-Belinchón, Stefano Scrobogna
Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the…
Global existence and exponential decay to equilibrium for DLSS-type equations
Hantaek Bae, Rafael Granero-Belinchón
In this paper, we deal with two logarithmic fourth order differential equations: the extended one-dimensional DLSS equation and its multi-dimensional analog. We show the global exi…