Alexandre, R.; Desvillettes, L.; Villani, C.; Wennberg, B. Entropy dissipation and long-range interactions. (English) Zbl 0968.76076 Arch. Ration. Mech. Anal. 152, No. 4, 327-355 (2000). Summary: We study Boltzmann collision operator for long-range interactions, i.e., without Grad’s angular cut-off assumption. We establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function, in a precise sense. Our estimate is optimal and gives a unified treatment of both the linear and nonlinear cases. We also give simple and self-contained proofs of several useful results that were scattered in previous works. As an application, we obtain estimates for Cauchy problem, and for the Landau approximation in plasma physics. Cited in 6 ReviewsCited in 145 Documents MSC: 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 82B40 Kinetic theory of gases in equilibrium statistical mechanics Keywords:smoothness of distribution function; Boltzmann collision operator; long-range interactions; entropy dissipation; estimates; Cauchy problem; Landau approximation; plasma physics PDFBibTeX XMLCite \textit{R. Alexandre} et al., Arch. Ration. Mech. Anal. 152, No. 4, 327--355 (2000; Zbl 0968.76076) Full Text: DOI