TY - JOUR
T1 - DISSIPATION AND SEMIGROUP ON Hkn
T2 - NON-CUTOFF LINEARIZED BOLTZMANN OPERATOR WITH SOFT POTENTIAL
AU - DENG, Dingqun
PY - 2020
Y1 - 2020
N2 - In this paper, we find that the linearized collision operator L of the non-cutoff
Boltzmann equation with soft potential generates a strongly continuous semigroup on Hkn, with
k, n ∈ R. In the theory of the Boltzmann equation without angular cutoff, the weighted Sobolev
space plays a fundamental role. The proof is based on pseudodifferential calculus, and, in general,
for a specific class of Weyl quantization, the L2 dissipation implies Hkn dissipation. This kind of
estimate is also known as Gårding's inequality.
AB - In this paper, we find that the linearized collision operator L of the non-cutoff
Boltzmann equation with soft potential generates a strongly continuous semigroup on Hkn, with
k, n ∈ R. In the theory of the Boltzmann equation without angular cutoff, the weighted Sobolev
space plays a fundamental role. The proof is based on pseudodifferential calculus, and, in general,
for a specific class of Weyl quantization, the L2 dissipation implies Hkn dissipation. This kind of
estimate is also known as Gårding's inequality.
KW - Boltzmann equation
KW - linearized collision operator
KW - pseudodifferential operator
KW - dissipation
KW - strongly continuous semigroup
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U2 - 10.1137/19M1263017
DO - 10.1137/19M1263017
M3 - 21_Publication in refereed journal
VL - 52
SP - 3093
EP - 3113
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 3
ER -