MATH 858A Special topics in analysis, Section: 0902: Long time dynamics of kinetic equations
Wednesdays 4-5pm, tenatitively in CSCAMM conference room A (4th floor of CSIC)
office: 4129 CSIC
My GnuPG public key id is: 69441DCC, which is available on public keyservers
Consider using public key encryption as a standard tool for secure communication.
This informal reading course will focus on the long time dynamics of
kinetic equations, probably with a focus on hypocoercivity. There will
probably not be too much emphasis on regularity theory unlesss there is
specific interest. Specific topics will be narrowed based on the
background and interests of the students, but the general plan is to
consider the following:
- A brief (non-rigorous) introduction to collisionless and collisional
kinetic equations, such as kinetic Fokker-Planck, Vlasov-Poisson,
Boltzmann and Vlasov-Poisson-Landau.
- A general reading and review of Villani's notes on hypocoercivity for the 2006 Proc. of the ICM (not
all the topics or the most general settings will be considered). These notes can be found here
Students may register for 1 credit if they want to just follow along
with the reading and make useful comments in discussions. Students may
register for 3 credits if they give a one hour presentation on a
specific sub-topic or do a computational study of kinetic equations of
some kind. The sub-topics will be in part determined by student areas of
interest and experience but example talks are:
- Specific sub-section(s) of Villani's notes on hypocoercivity.
- Present a specific work in the reference list that lead to or is
related to the main ideas of hypocoercivity.
- Topics on Landau damping in collisionless kinetic equations; for
example, to present Caglioti/Maffei's older work on Vlasov-Poisson,
Faou/Rousset's work on the HMF model or Young's recent work on
- Yan Guo's work on the Landau equation or Vlasov-Poisson-Landau in a
periodic box close to equilibrium.
- Topics in computational kinetic theory.
- A review of more non-standard kinetic models, such as relativistic
models, Cucker-Smale-type flocking models, quantum Boltzmann models etc.
- A related aspect of Desvillettes/Villani works, for example, the work
on Fokker-Planck or Villani's paper on Cercignani's conjecture.
- Regularity and well-posedness theory, for example, one of: global
well-posedness for Vlasov-Poisson in 3D, local regularity theory for
collisional kinetic theory models, instantaneous regularization results,
renormalized solutions for the Boltzmann equations.
- Organizational/introductory meeting in CSCAMM Conference Room A (4th floor of CSIC) on 4-5 Wednesday
- Sept 17/24: Sections 3-5 in Villani's notes
- Oct 1: Probably cancelled.
- Oct 8: Sam on logarithmic Sobolev inequalities and hypocoercivity in the entropic sense
- Oct 15: Jacob (probably) on Yan Guo's Landau equation in a periodic box
- Oct 22: Jacob (probably) on Yan Guo's Landau equation in a periodic box
- Oct 29: Either cancelled or Jacob (probably) on Yan Guo's Landau equation in a periodic box
- Nov 5: Either cancelled or Jacob (probably) on Yan Guo's Landau equation in a periodic box
- Nov 12: Scott on Cercignani's conjecture or Jacob on Yan Guo's Landau equation in a periodic box
- Nov 19: Iaonnis on hypoellipticity?
- Nov 26: Cancelled or Jacob on Landau damping in the collisionless Vlasov equations
- Dec 3: Luyu on kinetic models for flocking and collective behavior
- Dec 10: Michele Coti-Zelati on hypocoercive methods in fluid mechanics
- Dec 17: Probably cancelled