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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Hardy inequalities for the Landau equation - Maria
Gualdani (University of Texas Austin)
DTSTART;TZID=Europe/London:20220323T140000
DTEND;TZID=Europe/London:20220323T150000
UID:TALK171917AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171917
DESCRIPTION:Kinetic equations are used to describe evolution o
f interacting particles. The most famous kinetic e
quation is the Boltzmann equation: formulated by L
udwig Boltzmann in 1872\, this equation describes
motion of a large class of gases. Later\, in 1936\
, Lev Landau derived a new mathematical model for
motion of plasma. This latter equation was named t
he Landau equation. One of the main features of th
e Landau equation is nonlocality\, meaning that pa
rticles interact at large\, non-infinitesimal leng
th scales. Moreover\, the coefficients are singula
r and degenerate for large velocities. Many import
ant questions\, such as whether or not solutions b
ecome unbounded after a finite time\, are still un
answered due to their mathematical complexity. In
this talk we concentrate on the mathematical resul
ts of the homogeneous Landau equation. We will fir
st review existing results and open problems on gl
obal regularity versus blow-up in finite time. In
the second part of the talk we will focus on recen
t developments of regularity theory for an isotrop
ic version of the Landau equation. \n\nThis is a j
oint work with Nestor Guillen. \n
LOCATION:CMS\, MR13
CONTACT:Daniel Boutros
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