Narrow Results

This paper aims at the long-time behavior of non-autonomous 2D Navier–Stokes equations with a class of external forces which are $H$-valued measures in time. We first establish the well-posedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of $𝜀$-entropy for such uniform attractor in the standard energy phase space.

In this talk we present a brief summary of some recent results of the author on the subject of impulsive stochastic differential inclusions on Hilbert spaces. We also discuss briefly some problems of optimal control.

A well known vector measure version of the Radon-Nikodým theorem—comparing two vector measures— can also be interpreted in terms of factorization of an operator—the one associated to the first measure— through the one associated to the second one. Using several results published in recent years, we show the factorization version of this Radon-Nikodým theorem and its applications in the setting of the Operator Theory and the Harmonic Analysis.