caa a22 4500 467891524 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9039-5 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9039-5 Lu Xuguang Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People's Republic of China aut On the Boltzmann Equation for Fermi-Dirac Particles with Very Soft Potentials: Averaging Compactness of Weak Solutions [Elektronische Daten] [Xuguang Lu] The paper considers macroscopic behavior of a Fermi-Dirac particle system. We prove the L 1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi-Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ *|γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫0 π b(cos θ)sin 3θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff-Young inequality, the L ∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy. Springer Science + Business Media, Inc., 2006 Boltzmann equation nationallicence Fermi-Dirac particles nationallicence coulomb interaction nationallicence weak angular cutoff nationallicence averaging compactness nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 517-547 0022-4715 124:2-4<517 2006 124 10955 https://doi.org/10.1007/s10955-006-9039-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9039-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lu Xuguang Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 517-547 0022-4715 124:2-4<517 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer