• Boltzmann equation. conservation laws, H Theorem, basic estimates, hydrodynamic scalings, formal limit to the compressible Euler system.
• Velocity averaging. Renormalized solutions of the Boltzmann equation.
• Asymptotic methods (Hilbert and Chapman-Enskog expansions). The linearized Boltzmann operator.
• Incompressible hydrodynamic limits (formal results/small data results).
• Incompressible Euler limit of the Boltzmann equation (the relative entropy method).
• Incompressible Navier-Stokes limit of the Boltzmann equation.

Part I: Spectral and deterministic methods
Lorenzo Pareschi, Università di Ferrara, Italy

The Boltzmann Equation

Deterministic methods

Discrete velocity models; Derivation; Properties; Drawbacks; Examples; Spectral methods; Spectral-Fourier projection; Analysis of the kernel modes; Properties of the spectral method; Numerical results; Fast methods; Carleman representation; Periodization;Applications.

Non homogeneous case

Positive and Flux Conservative method (PFC); Coupling with the collision part; Time discretization; Time relaxed schemes; Numerical results.

Part II: Monte Carlo methods
G. Russo, Università di Catania, Italy

Monte Carlo methods

Random sampling; Direct simulation Monte Carlo methods; Nanbu's method and Bird's method.

Time Relaxed Monte Carlo methods

Time Relaxed Monte Carlo methods; Numerical results; Improved Time Relaxed Monte Carlo methods; Recursive Time Relaxed Monte Carlo; Hybrid Time Relaxed Monte Carlo; Numerical results.

K. Aoki (Kyoto, Japan)
"Fluid-dynamic limit of vapor flows with evaporation and condensation: Effect of a trace of noncondensable gas"

N. Ben Abdallah (Toulouse, France)
"Transport models for partially quantized systems"
"Diffusion in partially quantized systems"

A. Bobylev (Karlstad, Sweden)
"Inelastic Boltzmann Equation and high energy tails"

C. Cercignani (Milano, Italy)
"Time asymptotics for the Boltzmann equation with inelastic interactions"

L. Desvillettes (Cachan, France)
"Reaction-Diffusion systems in the context of reversible chemistry"

C. Marchioro (Roma, Italy)
"Hamiltonian models for a runaway charged particle"

J. Polewczak (Northridge, USA)
"On the spectrum of the linearized revised Enskog operator"

Posters

• Bagland V., The spatially homogeneous Landau-Fermi-Dirac equation: well-posedness for hard potentials, equilibrium states
• Barletti L., Salvarani F., A kinetic approach to dust coagulation
• Belleni-Morante A., Pieraccini S., Riganti R., Numerical treatment of a time dependent inverse problem in photon transport
• Brull S., The stationary Boltzmann equation for a two component gas in the slab
• Chane-Yook M., On a quantum kinetic equation linked to the Compton effect
• Conforto F., Groppi M., A. Jannelli, Detonation problems via the Boltzmann equation for reactive gas mixtures
• Dhamo E., Manzini C., The three dimensional Wigner-Poisson-Fokker-Planck problem: global-in-time, smooth solution
• Lisi M., Totaro S., Photon transport with a localized source
• Mathiaud J., Hydrodynamic limit in the context of sprays
• Mouhot , Rate of convergence to equlibrium for the spatially homogeneus Boltzmann equation
• Negulescu C., WKB based schemes for Schroedinger equation
• Olla P., Pignagnoli L., Forward and Backward Montecarlo approach for non-Markovian stochastic processes; an application to inertial particle transport in random velocity fields

Home Page

List of participants

NAME	AFFILIATION	e-mail
Adami Riccardo	Università Roma I	adami@mat.uniroma1.it
Aoki Kazuo	University Kyoto	aoki@aero.mbox.media.kyoto-u.ac.jp
Bagland Veronique	Université Toulouse	bagland@mip.ups-tlse.fr
Baranger Celine	ENS Cachan	celine.baranger@cmla.ens-cachan.fr
Barletti Luigi	Università Firenze	barletti@math.unifi.it
Ben Abdallah Naoufel	Université Toulouse	naoufel@mip.ups-tlse.fr
Bernhoff Niclas	University Karlstad	niclas.bernhoff@kau.se
Bisi Marzia	Università Milano	bisi@mat.unimi.it
Bobylev Alexander	University Karlstad	alexander.bobylev@kau.se
Borgioli Giovanni	Università Firenze	borgioli@ingfi1.ing.unifi.it
Boscarino Sebastiano	Università Catania	boscarino@dmi.unict.it
Brull Stephane	Université Aix-Marseille I	stephane.brull@wanadoo.fr
Cercignani Carlo	Politecnico Milano	carcer@mate.polimi.it
Chane-Yook Martine	INRIA Sophia Antipolis	martine.chane_yook@sophia.inria.fr
Conforto Fiammetta	Università Messina	fiamma@dipmat.unime.it
Desvillettes Laurent	ENS Cachan	laurent.devillettes@cmla.ens-cachan.fr
Dhamo Elidon	University Muenster	dhamo@math.uni-muenster.de
Foscari Piero	Università Ferrara	quartz@interfree.it
Frank Martin	Tech. University Darmstadt	mfrank@mathematik.tu-darmstadt.de
Frosali Giovanni	Università Firenze	frosali@dma.unifi.it
Goettlich Simone	Tech. University Darmstadt	goettlich@mathematik.tu-darmstadt.de
Golse Francois	ENS Paris	francois.golse@ens.fr
Groppi Maria	Università Parma	maria.groppi@ipruniv.cce.unipr.it
Jannelli Alessandra	Università Messina	jannelli@dipmat.unime.it
Lisi Meri	Università Firenze	lisi@math.unifi.it
Manzini Chiara	SNS Pisa	c.manzini@sns.it
Manzo Francesco	Università Roma I	manzof@mat.uniroma1.it
Marchioro Carlo	Università Roma I	marchior@mat.uniroma1.it
Mathiaud Julien	ENS Cachan	julien.mathiaud@cmla.ens-cachan.fr
Monaco Roberto	Politecnico Torino	roberto.monaco@polito.it
Mossberg Eva	University Karlstad	eva.mossberg@kau.se
Mouhot Clement	ENS Lyon	cmouhot@umppa.ens-lyon.fr
Negulescu Claudia	Universitè Toulouse	negulesc@mip.ups-tlse.fr
Neumann Lukas	University Wien	lukas.neumann@univie.ac.at
Pareschi Lorenzo	Università Ferrara	prl@dns.unife.it
Petersson Niclas	University Karlstad	niclas.petersson@kau.se
Pieraccini Sandra	Politecnico Torino	sandra.pieraccini@polito.it
Pignagnoli Luca	ISAC-CNR Università Milano	L.pignagnoli@isac.cnr.it
Polewczak Jacek	California State Northridge	jacek.polewczak@csun.edu
Pulvirenti Ada	Università Pavia	ada@dimat.unipv.it
Russo Giovanni	Università Catania	russo@dmi.unict.it
Saint Raymond Laure	Universite' Paris VI	saintray@ann.jussieu.fr
Salvarani Francesco	Università Pavia	salvaran@dimat.unipv.it
Santagati Pietro	Università Catania	psantagati@dmi.unict.it
Schaefer Matthias	Tech. University Darmstadt	mschaefer@mathematik.tu-darmstadt.de
Spiga Giampiero	Università Parma	giampiero.spiga@unipr.it
Toscani Giuseppe	Università Pavia	toscani@dimat.unipv.it
Totaro Silvia	Università Siena	totaro@unisi.it
Trazzi Stefano	Università Ferrara	trazzi@dm.unife.it
Vinerean Mirela Cristina	University Karlstad	mirela.vinerean@kau.se
Wondmagegne Yosief	Chalmers University Goteborg	wondma@math.chalmers.se