Asymptotic behaviors of the semigroup of the linearized Landau operator for the very soft and Coulomb potentials
• Jiawei SUN,
• Yakui WU
Jiawei SUN
Institute of Applied Physics and Computational Mathematics
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Yakui WU
Capital Normal University
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## Abstract

We study the asymptotic behaviors of the semigroup generated by the linearized Landau operator in the case of the very soft potentials and Coulomb potential. Compared with the hard potentials, Maxwellian molecules and moderately soft potentials, there is no spectral gap for the linearized Landau operator with the very soft and Coulomb potentials. By introducing a new decomposition of the linear Landau collision operator $L$ including an accretive operator and a relatively compact operator, we establish the complete spectrum structure for the linearized Landau operator with the very soft and Coulomb potentials and furthermore derive the time decay estimates of the corresponding semigroup in a weighted velocity space.

#### Peer review status:UNDER REVIEW

13 Jan 2021Submitted to Mathematical Methods in the Applied Sciences
15 Jan 2021Assigned to Editor
15 Jan 2021Submission Checks Completed
27 Jan 2021Reviewer(s) Assigned