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Conservative forms of Boltzmann’s collision operator: Landau revisited. (English) Zbl 0919.35140

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.

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