论文标题
弗拉索夫 - 波森系统解决方案的散射和渐近行为在高维
Scattering and Asymptotic Behavior of Solutions to the Vlasov-Poisson System in High Dimension
论文作者
论文摘要
我们考虑了尺寸$ d \ geq 4 $的排斥性弗拉索夫 - 波森系统。提出了相关电场的衰减速率的足够条件，可以保证大型数据解决方案的散射和确定为$ t \ to \ infty $。更具体地说，我们表明，在这种情况下，粒子分布函数的空间平均收敛，并建立了电场和宏观密度的精确渐近谱。还证明了沿相关的自由运输轨迹的粒子分布函数的$ l^\ infty $散射结果。最后，我们构建了显示这种渐近行为的小数据解决方案。这些解决方案不需要$ \ | f_0 \ | _ \ infty $或派生词的较小度，因为仅施加了分布功能的集成矩上的条件。
We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic behavior of large data solutions as $t \to \infty$. More specifically, we show that under this condition the spatial average of the particle distribution function converges, and we establish the precise asymptotic profiles of the electric field and macroscopic densities. An $L^\infty$ scattering result for the particle distribution function along the associated trajectories of free transport is also proved. Finally, we construct small data solutions that display this asymptotic behavior. These solutions do not require smallness of $\|f_0\|_\infty$ or derivatives, as only a condition on integrated moments of the distribution function is imposed.
