The Vlasov-Maxwell system: modified scattering and non-asymptotic completeness

In 1987, Glassey and Strauss exhibited solutions to the Vlasov-Maxwell system, arising from small and compactly supported data. In this talk, we will consider these solutions and show that the particle densities exhibit a modified scattering dynamic in the multi-species case. Moreover, in this setting, we show the non-asymptotic completeness, i.e., there exists at least one particle density that does not scatter to a linear solution at infinity.