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Organizing Committee
Kyoto University
Brown University
University of Wisconsin
Università di Ferrara
Ecole Normale Suptrieure
Abstract
The celebrated Boltzmann equation is the foundation of the kinetic theory for dilute collections of particles, which undergo elastic binary collisions. The Boltzmann theory is at the center of a series of multi-scaled physical models that connect microscopic multiparticle models to macroscopic fluid models such as the Navier-Stokes equations:
Particles → Boltzmann → Fluids
The first arrow refers the Boltzmann-Grad limit, while the second arrow refers to various hydrodynamic limits which lead to the fundamental equations of fluids. The Boltzmann theory therefore provides a practical tool and machinery for deriving macroscopic models in broad physical applications. Due to its importance, there has been an explosion of mathematical studies, both theoretical and numerical, for the Boltzmann equation.A major open problem that remains is to determine whether or not smooth initial data would lead to a unique global-in-time solution of the Boltzmann equation. Nevertheless, there have been exciting new developments in recent years. The focus of the program is to bring computational and theoretical people together to investigate problems of fundamental importance.
The first arrow refers the Boltzmann-Grad limit, while the second arrow refers to various hydrodynamic limits which lead to the fundamental equations of fluids. The Boltzmann theory therefore provides a practical tool and machinery for deriving macroscopic models in broad physical applications. Due to its importance, there has been an explosion of mathematical studies, both theoretical and numerical, for the Boltzmann equation.A major open problem that remains is to determine whether or not smooth initial data would lead to a unique global-in-time solution of the Boltzmann equation. Nevertheless, there have been exciting new developments in recent years. The focus of the program is to bring computational and theoretical people together to investigate problems of fundamental importance.
Problems
Problem 1: Boundary Effects.
Boundary effects play an important role in the dynamics of particles confined in a bounded region. Yet its mathematical study is at an early stage. This is due to the fact that solutions to the Boltzmann equation in general will develop singularities. The focus is to investigate the formation and propagation of singularities, both from numerical and theoretical points of view.
Problem 2: Hydrodynamic Limits.
There have been lots of studies of hydrodynamic limits of the Boltzmann equation. The focus in our program will be on error estimates and higher-order expansions of hydrodynamic limits both from the theoretical point of view and from the point of view of numerical simulation. Boundary and initial layer analysis for hydrodynamic limits, which has been barely studied, is an important area that is ready for investigation.
Problem 3: Boltzmann-Grad Limit.
There has been little mathematical work in this direction since the work of Lanford. The focus will be on boundary effects in the Boltzmann-Grad limit, and on the application of Lanford\'s proof to establish the Boltzmann-Grad limit for other particle systems of physical importance. Numerical simulations at the particle level will play an key role.
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Workshop Schedule
Monday, November 07, 2011
8:30 - 8:55 AM EST
Registration and Welcome Coffee
8:55 - 9:00 AM EST
Welcome - Jill Pipher, Director, ICERM
Location: 11th Floor Lecture Hall
9:00 - 9:45 AM EST
From the Vlasov-Maxwell-Boltzmann System to Incompressible viscous electro-magneto-hydrodynamics, part I - Laure Saint-Raymond, Ecole Normale Supérieure & University Paris 6
Location: 11th Floor Lecture Hall
10:00 - 10:30 AM EST
Coffee/Tea Break
Location: 11th Floor Collaborative Space
12:30 - 2:30 PM EST
Break for Lunch and Free Time
3:30 - 4:00 PM EST
Coffee/Tea Break
Tuesday, November 08, 2011
Tutorial Week Schedule
Monday, October 31, 2011
1:30 - 2:00 PM EDT
Coffee/Tea Break
Location: 11th Floor Collaborative Space
2:00 - 4:00 PM EDT
An introduction to Collisional (Boltzmann-type) models in Kinetic theory - Robert Strain, University of Pennsylvania
Location: 11th Floor Lecture Hall
Tuesday, November 01, 2011
2:30 - 3:00 PM EDT
Coffee/Tea Break
Location: 11th Floor Collaborative Space
Wednesday, November 02, 2011
2:30 - 3:00 PM EDT
Coffee/Tea Break
Location: 11th Floor Collaborative Space
Thursday, November 03, 2011
1:50 - 2:00 PM EDT
ICERM Long Term Visitor Group Photo
Location: 11th Floor Lecture Hall
Lecture Videos
Cory Hauck
Oak Ridge National Laboratory
November 7, 2011 • 12:00 AM
Rossana Marra
University of Rome Tor Vergata
November 9, 2011 • 12:00 AM
Irene Gamba
University of Texas at Austin
November 11, 2011 • 12:00 AM
Marshall Slemrod
University of Wisconsin
November 7, 2011 • 12:00 AM
Charles Levermore
University of Maryland
November 11, 2011 • 12:00 AM
