Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential

In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory. Based on these estimates, we give the precise time decay rate estimates on the semigroup gen...

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Veröffentlicht in:Science China. Mathematics Jg. 66; H. 1; S. 37 - 78
Hauptverfasser: Yang, Tong, Yu, Hongjun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beijing Science China Press 01.01.2023
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Boltzmann transport equation
Coulomb potential
Decay
Decay rate
Eigenvalues
Estimates
Fourier transforms
Linear operators
Linearization
Mathematics
Mathematics and Statistics
Perturbation theory
Semigroups
spectrum structure
Landau equation
Boltzmann equation
35Q20
47A10
time decay rate
ISSN:1674-7283, 1869-1862
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Zusammenfassung:In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory. Based on these estimates, we give the precise time decay rate estimates on the semigroup generated by the linearized Landau operator so that the optimal time decay rates of the nonlinear Landau equation follow. In addition, we present a similar result for the non-angular cutoff Boltzmann equation with soft potentials.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-020-1901-4