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SUMMARY:The Landau Equation\, Part 1 and Part 2 (copy) - Maria Gualdani (U
 niversity of Texas at Austin)
DTSTART:20220201T140000Z
DTEND:20220201T150000Z
UID:TALK169400@talks.cam.ac.uk
DESCRIPTION:Statistical physics originated after the development of molecu
 lar theory for matter. In molecular theory\, gas\, solid\, or liquid matte
 r are considered a collection of many identical interacting particles. Cla
 ssical mathematical methods\, such as differential equations that track th
 e motion of each particle\, became powerless for such large systems. Scien
 tists ventured into statistical and probabilistic methods to describe larg
 e ensembles of objects. After the pioneering work of Bernoulli\, Maxwell (
 1860) and Boltzmann (1868) used statistical physics to model the dynamics 
 of gases. Their first investigations laid the foundation of kinetic theory
  and resulted in formulating the general equation of continuity\, a partia
 l differential equation known today as the Boltzmann equation. The Boltzma
 nn equation is probabilistic: its solution represents the probability of f
 inding a particle at time t at position x with velocity v. Later\, in 1936
 \, Lev Landau derived from the Boltzmann equation a new kinetic model to d
 escribe the motion of particles in hot plasma. From the 1960s\, kinetic eq
 uations have been used to model dilute quantum particles that follow the F
 ermi-Dirac or Bose-Einstein statistics.\nThis tutorial will encompass the 
 existing mathematical theory of the Landau equation in both homogeneous an
 d inhomogeneous settings. We will focus on one of the most challenging ope
 n questions\, namely the global-in-time-regularity versus blow-up in finit
 e time. We will also briefly introduce the Landau-Fermi-Dirac equation and
  present open problems.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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