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SUMMARY:On solutions of the Vlasov-Poisson-Landau equations for slowly var
 ying in space initial data - Alexander Bobylev (Keldysh Institute of Appli
 ed Mathematics)
DTSTART:20220426T090000Z
DTEND:20220426T100000Z
UID:TALK171833@talks.cam.ac.uk
DESCRIPTION:The talk is devoted to analytical and numerical study of solut
 ions to the Vlasov-Poisson-Landau kinetic equations (VPLE) for distributio
 n functions with typical length L such that &epsilon\; = rD/L << 1\, where
  &nbsp\;rD &nbsp\;stands for the Debye radius. It is also assumed that the
  Knudsen number Kn = l/L = O(1)\, where l denotes the mean free pass of el
 ectrons. We use the standard model of plasma of electrons with a spatially
  homogeneous neutralizing background of infinitely heavy ions. The initial
  data is always assumed to be close to neutral. We study an asymptotic beh
 avior of the system for small &epsilon\; > 0. It is known that the formal 
 limit of VPLE at &epsilon\; = 0 does not describe a rapidly oscillating pa
 rt of the electrical field [1]. Our aim is to study the behavior of the &l
 dquo\;true&rdquo\; electrical field near this limit. We consider the probl
 em with standard isotropic in velocities Maxwellian initial conditions\, a
 nd show that there is almost no damping of these oscillations in the colli
 sionless case. An approximate formula for the electrical field is derived 
 and then confirmed numerically by using a simplified BGK-type model of VPL
 E. Another class of initial conditions that leads to strong oscillations h
 aving the amplitude of order O(1/&epsilon\;) is also considered. A formal 
 asymptotic expansion of solution in powers of &epsilon\; is constructed. N
 umerical solutions of that class are studied for different values of param
 eters &epsilon\; and Kn. The work is based on papers [1]\, [2].\n[1] &nbsp
 \;Bobylev A.V.\, &nbsp\;Potapenko I.F.\, &nbsp\;Long &nbsp\;wave asymptoti
 cs for Vlasov-Poisson-Landau kinetic equation\, J.Statist. Phys.\, 175 (20
 19)\, 1-18.[2] &nbsp\;Bobylev A.V.\, &nbsp\;Potapenko I.F.\, &nbsp\;On sol
 utions of the Vlasov-Poisson-Landau equations for slowly varying in space 
 initial data (submitted to Kinet. Relat. Models in Jan. 2022).
LOCATION:Seminar Room 1\, Newton Institute
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