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- W4386044559 abstract "Two fundamental models in plasma physics are given by the Vlasov-Poisson-Landau system and the compressible Euler-Poisson system which both capture the complex dynamics of plasmas under the self-consistent electric field interactions at the kinetic and fluid levels, respectively. Although there have been extensive studies on the long wave limit of the Euler-Poisson system towards Korteweg-de Vries equations, few results on this topic are known for the Vlasov-Poisson-Landau system due to the complexity of the system and its underlying multiscale feature. In this article, we derive and justify the Korteweg-de Vries equations from the Vlasov-Poisson-Landau system modelling the motion of ions under the Maxwell-Boltzmann relation. Specifically, under the Gardner-Morikawa transformation $$ (t,x,v)to (delta^{frac{3}{2}}t,delta^{frac{1}{2}}(x-sqrt{frac{8}{3}}t),v) $$ with $ varepsilon^{frac{2}{3}}leq deltaleq varepsilon^{frac{2}{5}}$ and $varepsilon>0$ being the Knudsen number, we construct smooth solutions of the rescaled Vlasov-Poisson-Landau system over an arbitrary finite time interval that can converge uniformly to smooth solutions of the Korteweg-de Vries equations as $deltato 0$. Moreover, the explicit rate of convergence in $delta$ is also obtained. The proof is obtained by an appropriately chosen scaling and the intricate weighted energy method through the micro-macro decomposition around local Maxwellians." @default.
- W4386044559 created "2023-08-22" @default.
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- W4386044559 date "2023-08-17" @default.
- W4386044559 modified "2023-10-16" @default.
- W4386044559 title "KdV limit for the Vlasov-Poisson-Landau system" @default.
- W4386044559 doi "https://doi.org/10.48550/arxiv.2308.08863" @default.
- W4386044559 hasPublicationYear "2023" @default.
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