Kac’s Program in Kinetic Theory (new preprint)

I have just uploaded on arXiv a joint work with Stéphane Mischler on “Kac’s Program in Kinetic Theory”. In this paper, we answer a set of questions raised by Mark Kac in his seminal paper Foundations of kinetic theory (Proc. Third Berkeley Symp. Math. Stat. & Prob., 1956) about the derivation of Boltzmann equations from many-particle jump processes.

UPDATE: We have just uploaded an announcement note, to appear shortly in the Comptes-rendus de l’Académie des Sciences de Paris.

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Cercignani’s conjecture

Carlo Cercignani (1983)

Carlo Cercignani 1983 (Photo credit Kazuo Aoki)

Soon will happen a Conference in memory of Carlo Cercignani at IHP, Paris 9-11 february which I am co-organizing together with François Bolley, Laurent Desvillettes and Silvia Lorenzani. Moreover several works quoted for the Fields medal 2010 of Cédric Villani are directly related and somehow motivated by the so-called Cercignani’s conjecture in kinetic theory.

As a tribute to Carlo Cercignani, one of founder of the modern mathematical kinetic theory and a great scientist, here is a short presentation about Cercignani’s conjecture. More details (including references and latest results about the conjecture) can be found in this review paper.

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New preprint “Factorization for non-symmetric operators and exponential H-theorem”

We have just preprinted together with Maria Pia Gualdani and Stephane Mischler a new paper entitled “Factorization for non-symmetric operators and exponential H-theorem”:

http://hal.archives-ouvertes.fr/ccsd-00495786

http://arxiv.org/abs/1006.5523

This is part of a long-term project (started with the paper hal-00076709) on how to obtain relaxation estimates in larger spaces than the usual “symmetrization” space for PDEs arising in statistical physics. A general abstract spectral theory is developped in order to enlarge the functional space of decay estimates for semigroups. Then applications are given for Fokker-Planck and linear(ized) Boltzmann equations (homogeneous and inhomogeneous). The main outcome of the paper is the proof of exponential convergence in the H-theorem for the full Boltzmann equation under a priori smoothness conditions. The detailed abstract can be found below.

Comments are welcome.

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Isaac Newton Institute programme on Partial Differential Equations in Kinetic Theories next fall

The Isaac Newton Institute at Cambridge University hosts a semester programme on Partial Differential Equations in Kinetic Theories next fall.

It is also still possible to apply for the conference Fluid-Kinetic Modelling in Biology, Physics and Engineering which is part of this programme (new deadline is 31 July 2010).

Class on Mathematical Kinetic Theory

Homepage of the class “Mathematical Topics in Kinetic Theory”

Part III course, Michaelmas term 2011, University of Cambridge

Contact: Email me or use this forum.

Course description (2011-2012)

Chapter 1 (version 10th of october 2011)

Example sheet I (version of 10th of october 2011)
Some links:

Some elements of history of Kinetic Theory (up to 2001).