TY - JOUR
T1 - Global well-posedness for the Fokker-Planck-Boltzmann equation in Besov-Chemin-Lerner type spaces
AU - Liu, Zhengrong
AU - Tang, Hao
PY - 2016/6/15
Y1 - 2016/6/15
N2 - 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.
AB - 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.
KW - Cauchy problem
KW - Cutoff assumption
KW - Fokker-Planck-Boltzmann equation
KW - Hard potential
KW - Littlewood-Paley theory
UR - http://www.scopus.com/inward/record.url?scp=84960532780&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84960532780&origin=recordpage
U2 - 10.1016/j.jde.2016.02.031
DO - 10.1016/j.jde.2016.02.031
M3 - RGC 21 - Publication in refereed journal
SN - 0022-0396
VL - 260
SP - 8638
EP - 8674
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 12
ER -