Ling-Bing He, Yulong Zhou
Published 2017-01-20Version 1
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 cut-off 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 cut-off approximation method, our method results in higher order of accuracy.
Global existence and full regularity of the Boltzmann equation without angular cutoff
Global solutions in $W_k^{ζ,p}L^\infty_TL^2_v$ for the Boltzmann equation without cutoff
From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries
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