Abstract
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.
| Original language | English |
|---|---|
| Journal | Science China Mathematics |
| Online published | 10 Mar 2022 |
| DOIs | |
| Publication status | Online published - 10 Mar 2022 |
Funding
The first author was supported by the Research Grants Council of the Hong Kong Special Administrative Region of the People’s Republic of China (Grant No. SRF2021-1S01) and National Natural Science Foundation of China (Grant No. 11971200). The second author was supported by National Natural Science Foundation of China (Grant No. 11871229) and the Project Supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme 2017. The authors thank the anonymous referees for their helpful comments on this paper.
Research Keywords
- spectrum structure
- time decay rate
- Landau equation
- Boltzmann equation
- BOLTZMANN-EQUATION
- EXPONENTIAL DECAY
- ANGULAR CUTOFF
- SYSTEM
- EXISTENCE
- LEVEL
- LIMIT