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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Can spectral gap form in soft potentials? - Renjun
Duan (Chinese University of Hong Kong)
DTSTART;TZID=Europe/London:20220113T143000
DTEND;TZID=Europe/London:20220113T153000
UID:TALK166651AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/166651
DESCRIPTION:In the talk I will consider the spectral gap for t
he linearized Boltzmann or Landau equation with so
ft potentials. It is known that the corresponding
collision operators admit only the degenerated spe
ctral gap. We rather prove the formation of spectr
al gap in the spatially inhomogeneous setting wher
e the space domain is bounded with an inflow bound
ary condition. The key strategy is to introduce a
new Hilbert space with an exponential weight funct
ion that involves the inner product of space and v
elocity variables and also has the strictly positi
ve upper and lower bounds. The action of the trans
port operator on such space-velocity dependent wei
ght function induces an extra non-degenerate relax
ation dissipation in large velocity that can be em
ployed to compensate the degenerate spectral gap a
nd hence give the exponential decay for solutions
in contrast with the sub-exponential decay in eith
er the spatially homogeneous case or the case of t
orus domain. The result reveals a new insight of h
ypocoercivity for kinetic equations with soft pote
ntials in the specified situation.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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