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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On solutions of the Vlasov-Poisson-Landau equation
s for slowly varying in space initial data - Alexa
nder Bobylev (Keldysh Institute of Applied Mathema
tics)
DTSTART;TZID=Europe/London:20220426T100000
DTEND;TZID=Europe/London:20220426T110000
UID:TALK171833AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171833
DESCRIPTION:The talk is devoted to analytical and numerical st
udy of solutions to the Vlasov-Poisson-Landau kine
tic equations (VPLE) for distribution functions wi
th typical length L such that &epsilon\; = rD/L <<
1\, where \;rD \;stands for the Debye r
adius. It is also assumed that the Knudsen number
Kn = l/L = O(1)\, where l denotes the mean free pa
ss of electrons. We use the standard model of plas
ma of electrons with a spatially homogeneous neutr
alizing background of infinitely heavy ions. The i
nitial data is always assumed to be close to neutr
al. We study an asymptotic behavior of the system
for small &epsilon\; > 0. It is known that the for
mal limit of VPLE at &epsilon\; = 0 does not descr
ibe a rapidly oscillating part of the electrical f
ield [1]. Our aim is to study the behavior of the
&ldquo\;true&rdquo\; electrical field near this li
mit. We consider the problem with standard isotrop
ic in velocities Maxwellian initial conditions\, a
nd show that there is almost no damping of these o
scillations in the collisionless case. An approxim
ate formula for the electrical field is derived an
d then confirmed numerically by using a simplified
BGK-type model of VPLE. Another class of initial
conditions that leads to strong oscillations havin
g the amplitude of order O(1/&epsilon\;) is also c
onsidered. A formal asymptotic expansion of soluti
on in powers of &epsilon\; is constructed. Numeric
al solutions of that class are studied for differe
nt values of parameters &epsilon\; and Kn. The wor
k is based on papers [1]\, [2].\n[1] \;Bobyle
v A.V.\, \;Potapenko I.F.\, \;Long
\;wave asymptotics for Vlasov-Poisson-Landau kinet
ic equation\, J.Statist. Phys.\, 175 (2019)\, 1-18
.[2] \;Bobylev A.V.\, \;Potapenko I.F.\,
\;On solutions 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
CONTACT:
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