High order approximation for the Boltzmann equation without angular cutoff
Lingbing He Yulong Zhou
Kinetic & Related Models 2018, 11(3): 547-596 doi: 10.3934/krm.2018024

In order to solve the Boltzmann equation numerically, in the present work, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator with angular cutoff and the Landau collision operator. As a first step, we prove the well-posedness theory for our approximate equation. Then in the next step we show the error estimate between the solutions to the approximate equation and the original equation. Compared to the standard angular cutoff approximation method, our method results in higher order of accuracy.

keywords: Homogeneous Boltzmann equation full-range interactions hard potentials high order approximation global solutions

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