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Dynamics of differentiation and integration operators on weighted spaces of entire functions

María J. Beltrán — 2014

Studia Mathematica

We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study their spectra. Special emphasis is put on exponential weights.

A lattice gas model for the incompressible Navier–Stokes equation

J. Beltrán;  C. Landim — 2008

Annales de l'I.H.P. Probabilités et statistiques

We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.

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