Javier Gómez-Serrano
Princeton University
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Publication
Featured researches published by Javier Gómez-Serrano.
Duke Mathematical Journal | 2016
Angel de Castro; Diego Córdoba; Javier Gómez-Serrano
Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equation for
Proceedings of the National Academy of Sciences of the United States of America | 2012
Angel de Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; Javier Gómez-Serrano
\alpha \in [1,2)
Mathematical Models and Methods in Applied Sciences | 2012
Javier Gómez-Serrano; Carl Graham; Jean-Yves Le Boudec
. We also show
Nonlinearity | 2014
Javier Gómez-Serrano; Rafael Granero-Belinchón
C^{\infty}
Journal of Mathematical Physics | 2012
Angel de Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; Javier Gómez-Serrano
regularity of their boundary for all
Philosophical Transactions of the Royal Society A | 2015
Diego Córdoba; Javier Gómez-Serrano; Andrej Zlatos
\alpha \in (0,2)
Archive for Rational Mechanics and Analysis | 2018
Angel de Castro; Diego Córdoba; Javier Gómez-Serrano
.
Advances in Complex Systems | 2012
Javier Gómez-Serrano; Jean-Yves Le Boudec
We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.
arXiv: Analysis of PDEs | 2016
Angel de Castro; Diego Córdoba; Javier Gómez-Serrano
The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into a random set of clusters too far apart to interact, and thereafter all opinions in every cluster converge to their barycenter. We then prove a mean-field limit result, propagation of chaos: as the number of peers goes to infinity in adequately started systems and time is rescaled accordingly, the opinion processes converge to i.i.d. nonlinear Markov (or McKean-Vlasov) processes; the limit opinion processes evolves as if under the influence of opinions drawn from its own instantaneous law, which are the unique solution of a nonlinear integro-differential equation of Kac type. This implies that the (random) empirical distribution processes converges to this (deterministic) solution. We then prove that, as time goes to infinity, this solution converges to a law concentrated on isolated opinions too far apart to interact, and identify sufficient conditions for the limit not to depend on the initial condition, and to be concentrated at a single opinion. Finally, we prove that if the equation has an initial condition with a density, then its solution has a density at all times, develop a numerical scheme for the corresponding functional equation, and show numerically that bifurcations may occur.
arXiv: Analysis of PDEs | 2015
Angel de Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; Javier Gómez-Serrano
We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the permeability is given by a nonnegative step function. We study the influence of different choices of the permeability and different boundary conditions (both at infinity and considering finite/infinite depth) in the development or prevention of singularities for short time. In the general case (inhomogeneous, confined) we prove a bifurcation diagram concerning the appearance or not of singularities when the depth of the medium and the permeabilities change. The proofs are carried out using a combination of classical analysis techniques and computer-assisted verification.