The Boltzmann Equation: In the Trail of Torsten Carleman
May 16 - May 20, 2022
After Boltzmann published his works on the kinetic theory of gases, and the equation that bears his name, in 1872, it took 60 years before T. Carleman gave the first proof of existence of solutions to this equation in a famous paper in Acta Mathematica. Carleman continued his research on this subject ever since, with the results of his investigations appearing in a posthumously edited book with important contributions by Carleson and Frostman in 1957, has been very influential in the subsequent development of the mathematical aspects of kinetic theory of gases. Equally important for the kinetic theory of gases was Leif Arkeryd’s paper from 1972, and his work also marked a new start of kinetic theory in Sweden. It is in celebration of Leif Arkeryd’s 80th birthday that this workshop is taking place.
The Boltzmann equation is a nonlinear integro-differential equation which is very challenging from mathematical point of view. The enormous progress that has been achieved in the past few decades is based on the development of general tools for PDE:s, functional analysis and probability theory, and a careful and innovative use of the particular structure of this equation.
The workshop brings some of the most prominent mathematicians working in this field, some with a long experience and some who are in the beginning of their career.
Seminars Scroll to the next upcoming seminar
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About the quasilinear approximation for Vlasov equation and related equations May 16 09:00 - 09:50 -
Two-temperature Navier-Stokes equations for a polyatomic gas and their boundary conditions (Online) May 16 09:50 - 10:30 Two-temperature Navier-Stokes equations for a polyatomic gas and their boundary conditions (Online)
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Linearized Boltzmann collision operators for multicomponent and polyatomic gases May 16 11:00 - 11:50 Linearized Boltzmann collision operators for multicomponent and polyatomic gases
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Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium May 16 13:30 - 14:20 Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium
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On Boltzmann type equations and approaches without averaging May 16 14:20 - 15:10 On Boltzmann type equations and approaches without averaging
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About equilibrium distributions for Boltzmann-like models (Online) May 16 15:40 - 16:20 About equilibrium distributions for Boltzmann-like models (Online)
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About the Lp theory for the non-cutoff Boltzmann equation May 17 09:00 - 09:50 About the Lp theory for the non-cutoff Boltzmann equation
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Some recent results on the spatially homogeneous quantum Boltzmann equation (Online) May 17 09:50 - 10:30 Some recent results on the spatially homogeneous quantum Boltzmann equation (Online)
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On a system of equations in the kinetic description of a condensed, homogeneous gas of bosons: local existence of re… May 17 11:00 - 11:50 On a system of equations in the kinetic description of a condensed, homogeneous gas of bosons: local existence of re…
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On solutions of the Vlasov-Poisson-Landau equations for slowly varying in space initial data May 17 13:30 - 14:20 On solutions of the Vlasov-Poisson-Landau equations for slowly varying in space initial data
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On the 2D Peskin problem (Online) May 17 14:20 - 15:00 On the 2D Peskin problem (Online)
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Stationary solutions to the Boltzmann equation past an obstacle in the hydrodynamic limit May 17 15:30 - 16:20 Stationary solutions to the Boltzmann equation past an obstacle in the hydrodynamic limit
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Quantum kinetic theory of the fermionic Hubbard model (Online) May 18 08:30 - 09:10 Quantum kinetic theory of the fermionic Hubbard model (Online)
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On the body size distributions of species. A kinetic approach May 18 09:10 - 09:50 On the body size distributions of species. A kinetic approach
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On the oscillatory behaviour of a bimonomeric nonlinear Becker-Döring type model for prion dynamics May 18 10:20 - 11:10 On the oscillatory behaviour of a bimonomeric nonlinear Becker-Döring type model for prion dynamics
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Boltzmann’s legacy in optimization and machine learning May 19 09:00 - 09:50 Boltzmann’s legacy in optimization and machine learning
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Some considerations on the particle approximation for the BGK model in a bounded domain (Online) May 19 09:50 - 10:30 Some considerations on the particle approximation for the BGK model in a bounded domain (Online)
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From the many-body fermionic dynamics to the Vlasov equation with singular interactions May 19 11:00 - 11:50 From the many-body fermionic dynamics to the Vlasov equation with singular interactions
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Fokker-Planck Multi-Species Equations in the Adiabatic Asymptotics May 19 13:30 - 14:20 Fokker-Planck Multi-Species Equations in the Adiabatic Asymptotics
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Interplay between geometry and topology in models of collective dynamics (Online) May 19 14:50 - 15:30 Interplay between geometry and topology in models of collective dynamics (Online)
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Diffusive limit for a Boltzmann-like equation with non-conserved momentum May 19 15:30 - 16:20 Diffusive limit for a Boltzmann-like equation with non-conserved momentum
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Partial Regularity in Time for the Landau Equation May 20 09:00 - 09:50 Partial Regularity in Time for the Landau Equation
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On the Boltzmann equation modeling a polyatomic gas (Online) May 20 09:50 - 10:30 On the Boltzmann equation modeling a polyatomic gas (Online)
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From Boltzmann to Hamilton-Jacobi May 20 11:00 - 11:50 From Boltzmann to Hamilton-Jacobi
Recordings
Participants
| Name | University | Country | Arrival and Departure |
|---|---|---|---|
| Franz Achleitner (Online) | University: Technische Universität Wien | Country: Austria | Arrival and Departure: |
| Ricardo Alonso | University: Texas A&M Qatar | Country: United States | Arrival and Departure: |
| Håkan Andreasson | University: Chalmers University of Technology / University of Gothenburg | Country: Sweden | Arrival and Departure: |
| Kazuo Aoki (Online) | University: National Cheng Kung University | Country: Taiwan | Arrival and Departure: |
| Leif Arkeryd | University: Chalmers University of Technology / University of Gothenburg | Country: Sweden | Arrival and Departure: |
| Anton Arnold | University: Vienna University of Technology | Country: Austria | Arrival and Departure: |
| Mohammmad Asadzadeh | University: Chalmers University of Technology / University of Gothenburg | Country: Sweden | Arrival and Departure: |
| Jens Bardarson | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: |
| Claude Bardos | University: Laboratoire JLLions and University of Paris | Country: France | Arrival and Departure: |
| Niclas Bernhoff | University: Karlstad University | Country: Sweden | Arrival and Departure: |
| Mirela Bernhoff (Online) | University: Karlstad University | Country: Sweden | Arrival and Departure: |
| Alexander Bobylev | University: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences | Country: Russia | Arrival and Departure: |
| Stéphane Brull (Online) | University: Institut de Mathématiques de Bordeaux | Country: France | Arrival and Departure: |
| Silvia Caprino (Online) | University: Retired from universita' Tor Vergata Roma | Country: Italy | Arrival and Departure: |
| Eric Carlen | University: Rutgers University | Country: United States | Arrival and Departure: |
| Kleber Carrapatoso Online | University: Ecole Polytechnique | Country: France | Arrival and Departure: |
| Frederique Charles (Online) | University: Sorbonne Université | Country: France | Arrival and Departure: |
| I-Kun Chen (Online) | University: National Taiwan University | Country: Taiwan | Arrival and Departure: |
| Pierre Degond (Online) | University: Institut de Mathématiques de Toulouse | Country: France | Arrival and Departure: |
| Laurent Desvillettes (Online) | University: Université de Paris, IMJ-PRG | Country: France | Arrival and Departure: |
| Miguel Escobedo | University: Universidad del Pais Vasco | Country: Italy | Arrival and Departure: |
| Raffaele Esposito | University: Università dell'Aquila | Country: Italy | Arrival and Departure: |
| Josephine Evans | University: University of Warwick | Country: United Kingdom | Arrival and Departure: |
| Klemens Fellner | University: University of Graz | Country: Austria | Arrival and Departure: |
| Francis Filbet | University: University Toulouse | Country: France | Arrival and Departure: |
| Irene M. Gamba | University: The University of Texas at Austin | Country: United States | Arrival and Departure: |
| François Golse | University: Ecole polytechnique | Country: France | Arrival and Departure: |
| Maria Pia Gualdani | University: The University of Texas at Austin | Country: United States | Arrival and Departure: |
| Lingbing He (Online) | University: Tsinghua University | Country: China | Arrival and Departure: |
| Cyril Imbert (Online) | University: CNRS & ENS | Country: France | Arrival and Departure: |
| Pierre-Emmanuel Jabin (Online) | University: Pennsylvania State University | Country: United States | Arrival and Departure: |
| Hung-Wen Kuo (Online) | University: National Cheng Kung University | Country: Taiwan | Arrival and Departure: |
| He Lingbing | University: Tsinghua University | Country: China | Arrival and Departure: |
| Tai Ping Liu (Online) | University: Stanford University and Academia Sinica, Taipei | Country: United States / Taiwan | Arrival and Departure: |
| Bertrand Lods (Online) | University: University of Turin | Country: Italy | Arrival and Departure: |
| Xuguang Lu Online | University: Tsinghua University | Country: China | Arrival and Departure: |
| Jani Lukkarinen Online | University: University of Helsinki | Country: Finland | Arrival and Departure: |
| Rossana Marra | University: Universita di Roma Tor Vergata | Country: Italy | Arrival and Departure: |
| Dawan Mustafa | University: University of Borås | Country: Sweden | Arrival and Departure: |
| Anne Nouri | University: Université d'Aix-Marseille | Country: France | Arrival and Departure: |
| Lorenzo Pareschi | University: University of Ferrara | Country: Italy | Arrival and Departure: |
| Milana Pavić-Čolić (Online) | University: University of Novi-Sad | Country: Russia | Arrival and Departure: |
| Natasa Pavlovic (Online) | University: University of Texas at Austin | Country: United States | Arrival and Departure: |
| Mario Pulvirenti (Online) | University: Universita di Roma, Sapienza | Country: Italy | Arrival and Departure: |
| Chiara Saffirio | University: University of Basel | Country: China | Arrival and Departure: |
| Laure Saint-Raymond | University: IHES | Country: France | Arrival and Departure: |
| Lars Söderholm | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: |
| Robert Strain (Online) | University: University of Pennsylvania | Country: United States | Arrival and Departure: |
| Giuseppe Toscani | University: University of Pavia | Country: Italy | Arrival and Departure: |
| Isabelle Tristani (Online) | University: Ecole Normale Supérieure, Paris | Country: France | Arrival and Departure: |
| Bernt Wennberg | University: Chalmers University of Technology / University of Gothenburg | Country: Sweden | Arrival and Departure: |
| Yosief Wondmagegne | University: Karlstad University | Country: Sweden | Arrival and Departure: |
| Shih-Hsien Yu (Online) | University: Institute of Mathematics, Academia Sinica, Taipei | Country: Taiwan | Arrival and Departure: |