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SUMMARY:Hardy inequalities for the Landau equation - Maria Gualdani (Unive
 rsity of Texas Austin)
DTSTART:20220323T140000Z
DTEND:20220323T150000Z
UID:TALK171917@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:Kinetic equations are used to describe evolution of interactin
 g particles. The most famous kinetic equation is the Boltzmann equation: f
 ormulated by Ludwig Boltzmann in 1872\, this equation describes motion of 
 a large class of gases. Later\, in 1936\, Lev Landau derived a new mathema
 tical model for motion of plasma. This latter equation was named the Landa
 u equation. One of the main features of the Landau equation is nonlocality
 \, meaning that particles interact at large\, non-infinitesimal length sca
 les. Moreover\, the coefficients are singular and degenerate for large vel
 ocities. Many important questions\, such as whether or not solutions becom
 e unbounded after a finite time\, are still unanswered due to their mathem
 atical complexity. In this talk we concentrate on the mathematical results
  of the homogeneous Landau equation. We will first review existing results
  and open problems on global regularity versus blow-up in finite time. In 
 the second part of the talk we will focus on recent developments of regula
 rity theory for an isotropic version of the Landau equation. \n\nThis is a
  joint work with Nestor Guillen. \n
LOCATION:CMS\, MR13
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