Villani, Cédric Conservative forms of Boltzmann’s collision operator: Landau revisited. (English) Zbl 0919.35140 M2AN, Math. Model. Numer. Anal. 33, No. 1, 209-227 (1999). Summary: We show that Boltzmann’s collision operator \[ Q(f, f)= {1\over 2} \int_{\mathbb{R}^N} dv_* \int_{S^{N-1}} d\omega B(v-v_*, \omega)(f' f_*'- ff_*) \] can be written explicitly in divergence and double divergence forms. These conservative formulations may be of interest for both theoretical and numerical purposes. We give an application to the asymptotics of grazing collisions. Cited in 7 Documents MSC: 35Q72 Other PDE from mechanics (MSC2000) 82C40 Kinetic theory of gases in time-dependent statistical mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics Keywords:Boltzmann’s collision operator; asymptotics of grazing collisions × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link