论文标题
具有较小的分布函数的弗拉索夫 - 马克斯韦系统解决方案解决方案的全局存在和修饰的散射
Global existence and modified scattering for the solutions to the Vlasov-Maxwell system with a small distribution function
论文作者
论文摘要
本文的目的是双重的。在第一部分中，我们提供了具有较小初始分布函数的Vlasov-Maxwell系统的全球解决方案存在的新证明。我们的方法依赖于矢量场方法，以及电磁场的Glassey-Strauss分解，并且不需要对麦克斯韦场上的初始数据或小假设进行任何支持限制。与以前在Vlasov Systems中的作品相反，我们不会修改线性换向器，而是避免了许多技术困难。 在本文的第二部分中，我们证明了这些解决方案的修改后散射结果。更确切地说，我们获得电磁场具有沿未来的无效无穷大的辐射场，并在很大程度上接近了真空麦克斯韦方程的平滑解决方案。至于vlasov-Poisson系统，在约束中，分布函数沿自由相对论传输方程的特性的修改收敛到新的密度函数。为了定义这些对数校正，我们确定有效的渐近洛伦兹力。通过考虑根据渐近洛伦兹力的衍生物定义的线性换向器的对数修改，我们最终证明了极限分布函数的较高阶段的规律性结果。
The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods, together with the Glassey-Strauss decomposition of the electromagnetic field, and does not require any support restriction on the initial data or smallness assumption on the Maxwell field. Contrary to previous works on Vlasov systems in dimension $3$, we do not modify the linear commutators and avoid then many technical difficulties. In the second part of this paper, we prove a modified scattering result for these solutions. More precisely, we obtain that the electromagnetic field has a radiation field along future null infinity and approaches, for large time, a smooth solution to the vacuum Maxwell equations. As for the Vlasov-Poisson system, in constrast, the distribution function converges to a new density function along modifications of the characteristics of the free relativistic transport equation. In order to define these logarithmic corrections, we identify an effective asymptotic Lorentz force. By considering logarithmical modifications of the linear commutators, defined in terms of derivatives of the asymptotic Lorentz force, we finally prove higher order regularity results for the limit distribution function.
