Modified scattering for the Vlasov–Poisson system
Modified scattering for the Vlasov–Poisson system
复制标题
Vlasov-Poisson 系统的修正散射
DOI：
10.1088/0951-7715/29/9/2755
复制
发表时间：
2016
期刊：
影响因子：
1.7
通讯作者：
Soonsik Kwon
中科院分区：
文献类型：
--
作者：
Sun;Soonsik Kwon
研究了Vlasov-Poisson方程组色散解的渐近性态。由于长的相互作用范围，我们不期望线性散射（Choi S-H和Ha S-Y 2011 SIAM J. Math. Anal. 43 2050-77）。相反，我们证明了一个修改后的散射结果（或长距离散射结果）的小和分散的解决方案。我们找到一个准自由的前向轨迹，使沿着轨迹，解决方案有一个渐近极限。我们提取Duhamel项的对数增长部分，将其吸收到准自由轨线中，然后剩余部分享受更快的衰减，从而获得渐近状态。在本文中，当没有混淆时，我们简化了范数的符号。例如，我们表示Lp=Lx，vp为全局范数。我们将把C表示为一个一般常数，它随行而变化，并且与大时间T无关。当存在常数C使得A <$CB时，我们也使用符号A <$B。
We study the asymptotic behavior of dispersing solutions to the Vlasov–Poisson system. Due to long interaction range, we do not expect linear scattering (Choi S-H and Ha S-Y 2011 SIAM J. Math. Anal. 43 2050–77). Instead, we prove a modified scattering result (or long range scattering result) of small and dispersing solutions. We find a quasi-free forward trajectory so that along the trajectory, the solution has an asymptotic limit. We extract the logarithmic growth part of the Duhamel term, and absorb it into the quasi-free trajectory, then the remaining part enjoys faster decay so as to obtain the asymptotic state. Throughout this paper, we simplify notation of norms when there is no confusion. For example, we denote Lp=Lx,vp for global norms. We will denote C as a generic constant which varies from lines to lines and is independent of large time T. We also use the symbol A≲B when there is a constant C such that A⩽CB.