Searcharxiv⌕ Search

arXiv subjects

E. Terraneo

Publications and source records attributed to E. Terraneo.

5 recordsLinked to original sources
arXiv2025

Fokker--Planck equations and n--dimensional Poincar\'e inequalities for isotropic densities

We consider new connections between the problem of trend to equilibrium for the n-dimensional Fokker--Planck equation of statistical physics, and weighted Poincar\'e inequality. To this aim we consider a class of n-dimensional Fokker--Planck equations with variable isotropic coefficient of diffusion and drift, inspired by the analogous one-dimensional Fokker--Planck equation appearing when studying the evolution of wealth distribution.

math.AP↗
arXiv2025

Global Regularity to the liquid crystal flows of Q-tensor model

In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when the initial data are sufficiently small, improving a result in Xiao's paper [J. Differ. Equations 2017]. The key tool of the proof is a {maximum principle.} Then, we establish also a result of continuous dependence of solutions on the initial data. Finally, if $U=\R^3,$ based on a result of Du, Hu and Wang [Arch. Rational Mech. Anal. 2020], we give an interesting regularity criterium just via the $\dot{B}^{-1}_{\infty,\infty}$ norm of $u$ and the $L^\infty$ norm of the initial data $Q_0$.

math.AP↗
arXiv2011

The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium

This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [A. Pulvirenti and G. Toscani. J. Statist. Phys., 114(5-6):1453--1480, 2004], when the equilibrium distribution function is a heavy-tailed Lévy-type distribution with infinite variance. We prove that solutions in an appropriate domain of attraction of the equilibrium distribution converge to solutions of a Fokker-Planck equation with a fractional diffusion operator.

math.AP↗
arXiv2008

Strong Convergence towards self-similarity for one-dimensional dissipative Maxwell models

We prove the propagation of regularity, uniformly in time, for the scaled solutions of one-dimensional dissipative Maxwell models. This result together with the weak convergence towards the stationary state proven by Pareschi and Toscani in 2006 implies the strong convergence in Sobolev norms and in the L^1 norm towards it depending on the regularity of the initial data. In the case of the one-dimensional inelastic Boltzmann equation, the result does not depend of the degree of inelasticity. This generalizes a recent result of Carlen, Carrillo and Carvalho (arXiv:0805.1051v1), in which, for weak inelasticity, propagation of regularity for the scaled inelastic Boltzmann equation was found by means of a precise control of the growth of the Fisher information.

math.AP↗