The large amplitude solution of the Boltzmann equation with soft potential
SCIE
SCOPUS
- Title
- The large amplitude solution of the Boltzmann equation with soft potential
- Authors
- Gyounghun Ko; Donghyun Lee; Kwanghyuk Park
- Date Issued
- 2022-01
- Publisher
- Academic Press
- Abstract
- In this paper, we deal with the (angular cut-off) Boltzmann equation with soft potential (-3 < gamma < 0). In particular, we construct a unique global solution in L-x,v(infinity) which converges to global equilibrium asymptot-ically provided that initial data has a large amplitude but with sufficiently small relative entropy. Because frequency multiplier is not uniformly positive anymore, unlike hard potential case, time-involved veloc-ity weight will be used to derive sub-exponential decay of the solution. Motivated by recent development of L-2-L-infinity approach also, we introduce some modified estimates of quadratic nonlinear terms. Linearized collision kernel will be treated in a subtle manner to control singularity of soft potential kernel. (C) 2021 Elsevier Inc. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/110902
- DOI
- 10.1016/j.jde.2021.10.041
- ISSN
- 0022-0396
- Article Type
- Article
- Citation
- Journal of Differential Equations, vol. 307, no. 15, page. 297 - 347, 2022-01
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