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European Mathematical Society Publishing House
2024-03-28 17:34:44
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=13&iss=3&update_since=2024-03-28
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
13
1997
3
Diffusive limit for finite velocity Boltzmann kinetic models
Pierre-Louis
Lions
Univ de Paris IX Dauphine, PARIS CEDEX 05, FRANCE
Giuseppe
Toscani
Università di Pavia, PAVIA, ITALY
We investigate in the diff usive scaling the limit to the macroscopic description of fi nite- velocity Boltzmann kinetic models, where the rate coeffi cient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the fl ux vanishes while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so -called Rosseland approximation in radiative transfer theory .
General
473
513
10.4171/RMI/228
http://www.ems-ph.org/doi/10.4171/RMI/228
A generalization of a theorem by Kato on Navier-Stokes equations
Marco
Cannone
Université Paris 7, PARIS CEDEX 05, FRANCE
We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in $C(|0, \infty); L^3 (\mathbb R^3)$. More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theorem on existence of self-similar solutions for the Navier-Stokes equations.
General
515
541
10.4171/RMI/229
http://www.ems-ph.org/doi/10.4171/RMI/229
Some generalized Coxeter groups and their orbifolds
Marcel
Hagelberg
Université Paul Sabatier, TOULOUSE CEDEX 4, FRANCE
Rubén
Hidalgo
Universidad Técnica Federico Santa María, VALPARAÍSO, CHILE
In this note we construct examples of geometric 3-orbifolds with (orbifold) fundamental group isomorphic to a ($\mathbb Z$- extension of a) generalized Coxeter group. Some of these orbifolds have either euclidean spherical or hyperbolic structure. As an application we obtain an alternative proof of theorem 1 of Hagelberg, Maclaughlan and Rosenberg in [5]. We also obtain a similar result for generalized Coxeter groups .
General
543
566
10.4171/RMI/230
http://www.ems-ph.org/doi/10.4171/RMI/230
Estimates on the solution of an elliptic equation related to Brownian motion with drift (II)
Joseph
Conlon
University of Michigan, ANN ARBOR, UNITED STATES
Peder
Olsen
University of Michigan, ANN ARBOR, UNITED STATES
General
567
711
10.4171/RMI/231
http://www.ems-ph.org/doi/10.4171/RMI/231