Global well-posedness for the Fokker-Planck-Boltzmann equation in Besov-Chemin-Lerner type spaces
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Pages (from-to) | 8638-8674 |
Journal / Publication | Journal of Differential Equations |
Volume | 260 |
Issue number | 12 |
Publication status | Published - 15 Jun 2016 |
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Abstract
In this paper, motivated by [16], we use the Littlewood-Paley theory to establish some estimates on the nonlinear collision term, which enable us to investigate the Cauchy problem of the Fokker-Planck-Boltzmann equation. When the initial data is a small perturbation of the Maxwellian equilibrium state, under the Grad's angular cutoff assumption, the unique global solution for the hard potential case is obtained in the Besov-Chemin-Lerner type spaces C([0, ∞); L~ξ 2(B2,r s)) with 1 ≤ r ≤ 2 and s > 3/2 or s = 3/2 and r = 1. Besides, we also obtain the uniform stability of the dependence on the initial data.
Research Area(s)
- Cauchy problem, Cutoff assumption, Fokker-Planck-Boltzmann equation, Hard potential, Littlewood-Paley theory
Citation Format(s)
Global well-posedness for the Fokker-Planck-Boltzmann equation in Besov-Chemin-Lerner type spaces. / Liu, Zhengrong; Tang, Hao.
In: Journal of Differential Equations, Vol. 260, No. 12, 15.06.2016, p. 8638-8674.
In: Journal of Differential Equations, Vol. 260, No. 12, 15.06.2016, p. 8638-8674.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review