TY - JOUR
T1 - Non-cutoff Boltzmann equation with polynomial decay perturbations
AU - ALONSO, Ricardo
AU - MORIMOTO, Yoshinori
AU - SUN, Weiran
AU - YANG, Tong
N1 - Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).
PY - 2021/1/15
Y1 - 2021/1/15
N2 - The Boltzmann equation without the angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian and decays algebraically in the velocity variable. We obtain a well-posedness theory in the perturbative framework for both mild and strong angular singularities. The three main ingredients in the proof are the moment propagation, the spectral gap of the linearized operator, and the regularizing effect of the linearized operator when the initial data is in a Sobolev space with a negative index. A carefully designed pseudo-differential operator plays a central role in capturing the regularizing effect. In addition, some intrinsic symmetry with respect to the collision operator and an intrinsic functional in the coercivity estimate are essentially used in the commutator estimates for the collision operator with velocity weights.
AB - The Boltzmann equation without the angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian and decays algebraically in the velocity variable. We obtain a well-posedness theory in the perturbative framework for both mild and strong angular singularities. The three main ingredients in the proof are the moment propagation, the spectral gap of the linearized operator, and the regularizing effect of the linearized operator when the initial data is in a Sobolev space with a negative index. A carefully designed pseudo-differential operator plays a central role in capturing the regularizing effect. In addition, some intrinsic symmetry with respect to the collision operator and an intrinsic functional in the coercivity estimate are essentially used in the commutator estimates for the collision operator with velocity weights.
KW - Coercivity
KW - Commutator estimates
KW - Moment propagation
KW - Regularizing effect
KW - Spectral gap
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U2 - 10.4171/RMI/1206
DO - 10.4171/RMI/1206
M3 - 21_Publication in refereed journal
VL - 37
SP - 189
EP - 292
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
SN - 0213-2230
IS - 1
ER -