arXiv subjects

Carlo Boldrighini

Publications and source records attributed to Carlo Boldrighini.

4 recordsLinked to original sources

arXiv2017

On the blow-up of some complex solutions of the 3-d Navier-Stokes Equations: Theoretical Predictions and Computer simulations

We consider some complex-valued solutions of the Navier-Stokes equations in $R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the "fluid" remains quiet.

math-ph↗

arXiv2017

Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations

We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".

physics.flu-dyn↗

arXiv2015

Weak dependence for a class of local functionals of Markov chains on $\mathbb{Z}^d$

In some papers on infinite Markov chains in $\mathbb{Z}^d$, and notably in the work of R.A. Minlos and collaborators, one can prove the existence of a spectral gap for a suitable subspace of local functions. We consider functions of the type $f(\widehat η)$, where $\widehat η= \{η_{t}\}_{t=0}^{\infty}$ is the sequence of the states, and $f$ is local. In the case of a simple example of random walk in random environment with mutual interaction we show that there is a natural class of functions $f$, related to the Hölder continuos functions $\mathcal C^α$on the torus $T^{1}$, with $α\in (0,1)$ large enough, depending on the spectral gap, for which the Central Limit Theorem holds for the sequence $f(S^{k}\widehat η)$, $k=0,1,\ldots$, where $S$ is the time shift.

math-ph↗

arXiv2010

Navier-Stokes equations on the flat cylinder with vorticity production on the boundary

We study the two-dimensional Navier-Stokes system on a flat cylinder with the usual Dirichlet boundary conditions for the velocity field u. We formulate the problem as an infinite system of ODE's for the natural Fourier components of the vorticity, and the boundary conditions are taken into account by adding a vorticity production at the boundary. We prove equivalence to the original Navier-Stokes system and show that the decay of the Fourier modes is exponential for any positive time in the periodic direction, but it is only power-like in the other direction.

math-ph↗