×

Entropy dissipation and long-range interactions. (English) Zbl 0968.76076

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.

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
PDFBibTeX XMLCite
Full Text: DOI