Abstract
In this paper, we give the existence theory and the optimal time convergence rates of the solutions to the Boltzmann equation with frictional force near a global Maxwellian. We generalize our previous results on the same problem for hard sphere model into both hard potential and soft potential case. The main method used in this paper is the classic energy method combined with some new time-velocity weight functions to control the large velocity growth in the nonlinear term for the case of interactions with hard potentials and to deal with the singularity of the cross-section at zero relative velocity for the soft potential case. © 2014 Elsevier Inc.
| Original language | English |
|---|---|
| Pages (from-to) | 481-503 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 417 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Sept 2014 |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to <a href="mailto:[email protected]">[email protected]</a>.Funding
This work is partially supported by NSFC (Grant No. 11101376 ).
Research Keywords
- Boltzmann equation
- Hard potential
- Soft potential
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