# American Institute of Mathematical Sciences

June  2018, 11(3): 547-596. doi: 10.3934/krm.2018024

## High order approximation for the Boltzmann equation without angular cutoff

 1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 2 School of Mathematics, Yunnan Normal University, Kunming 650500, China

* Corresponding author: Yulong Zhou

Received  March 2017 Revised  September 2017 Published  March 2018

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.

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