Hilbert expansion from the Boltzmann equation to relativistic fluids
J Speck, RM Strain - Communications in mathematical physics, 2011 - Springer
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a
Hilbert expansion. More specifically, we prove the existence of local solutions to the …
Hilbert expansion. More specifically, we prove the existence of local solutions to the …
From Boltzmann's equation to the incompressible Navier–Stokes–Fourier system with long-range interactions
D Arsénio - Archive for Rational Mechanics and Analysis, 2012 - Springer
We establish a rigorous demonstration of the hydrodynamic convergence of the Boltzmann
equation towards a Navier–Stokes–Fourier system under the presence of long-range …
equation towards a Navier–Stokes–Fourier system under the presence of long-range …
Compactness in kinetic transport equations and hypoellipticity
D Arsénio, L Saint-Raymond - Journal of Functional Analysis, 2011 - Elsevier
We establish improved hypoelliptic estimates on the solutions of kinetic transport equations,
using a suitable decomposition of the phase space. Our main result shows that the relative …
using a suitable decomposition of the phase space. Our main result shows that the relative …
On the Global Existence of Mild Solutions to the Boltzmann Equation for Small Data in L D
D Arsénio - Communications in mathematical physics, 2011 - Springer
We develop a new theory of existence of global solutions to the Boltzmann equation for
small initial data. These new mild solutions are analogous to the mild solutions for the …
small initial data. These new mild solutions are analogous to the mild solutions for the …
[HTML][HTML] A new approach to velocity averaging lemmas in Besov spaces
D Arsénio, N Masmoudi - Journal de Mathématiques Pures et Appliquées, 2014 - Elsevier
We develop a new approach to velocity averaging lemmas based on the dispersive
properties of the kinetic transport operator. This method yields unprecedented sharp results …
properties of the kinetic transport operator. This method yields unprecedented sharp results …
Regularity of renormalized solutions in the Boltzmann equation with long‐range interactions
D Arsénio, N Masmoudi - Communications on Pure and …, 2012 - Wiley Online Library
It is well‐established that renormalized solutions of the Boltzmann equation enjoy some kind
of regularity, or at least compactness, in the velocity variable when the angular collision …
of regularity, or at least compactness, in the velocity variable when the angular collision …
Concentrations in kinetic transport equations and hypoellipticity
D Arsénio, L Saint-Raymond - arXiv preprint arXiv:1005.1547, 2010 - arxiv.org
We establish improved hypoelliptic estimates on the solutions of kinetic transport equations,
using a suitable decomposition of the phase space. Our main result shows that the relative …
using a suitable decomposition of the phase space. Our main result shows that the relative …
[PDF][PDF] A NEW APPROACH TO VELOCITY AVERAGING LEMMAS IN BESOV SPACES
DARS ÉNIO, N MASMOUDI - arXiv preprint arXiv:1206.6659, 2012 - Citeseer
arXiv:1206.6659v1 [math.AP] 28 Jun 2012 Page 1 arXiv:1206.6659v1 [math.AP] 28 Jun 2012
A NEW APPROACH TO VELOCITY AVERAGING LEMMAS IN BESOV SPACES DIOGO ARS …
A NEW APPROACH TO VELOCITY AVERAGING LEMMAS IN BESOV SPACES DIOGO ARS …
[PDF][PDF] CONCENTRATIONS IN KINETIC TRANSPORT EQUATIONS AND HYPOELLIPTICITY
DARS ÉNIO, L SAINT-RAYMOND - arXiv preprint arXiv:1005.1547, 2010 - Citeseer
We establish improved hypoelliptic estimates on the solutions of kinetic transport equations,
using a suitable decomposition of the phase space. Our main result shows that the relative …
using a suitable decomposition of the phase space. Our main result shows that the relative …