论文标题
弗拉索夫 - 波森 - 波尔兹曼系统的规律性无角截止
Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff
论文作者
论文摘要
在本文中，我们研究了整个空间中两个物种的血浆颗粒的非切割vlasov-poisson-boltzmann系统的规律性，$ \ mathbb {r}^3 $具有硬势。附近的麦克斯韦解决方案的存在以[15]的软潜力而闻名。但是，这些解决方案的平滑效果一直是一个具有挑战性的开放问题。我们建立了全球存在和正规化对凯奇问题的效果，以巨大的时间衰减，以实现艰苦的潜力。因此，对于$（t，x，v）$，在任何积极的时间$ t> 0 $的$（t，x，v）$方面都是平稳的。这为Vlasov-Poisson-Boltzmann系统提供了规律性，该系统具有与Boltzmann方程相似的平滑效果。该证明基于伪差分计算的时间加权能量法的构建。
In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions is known for soft potential from [15]. However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0$. This gives the regularity to Vlasov-Poisson-Boltzmann system, which enjoys a similar smoothing effect as Boltzmann equation. The proof is based on the time-weighted energy method building also upon the pseudo-differential calculus.
