91ÌÒÉ«

The Vlasov-Maxwell system is a PDE that models a collisionless relativistic plasma. More precisely, it governs the dynamic of a charged particle density f and an electromagnetic field (E,B). Due to the movement of the charged particle, the electromagnetic field depends on f through Maxwell equations, and induces a non-linearity in the system. While this system is similar to the Vlasov-Poisson equation, the Maxwell equations makes the study more complex and we cannot use elliptic regularity arguments. Still, one of the first result was given by Glassey and Strauss in 1987. In their article, they considered small and compactly supported data, and proved the existence (and uniqueness) of a global classical solution.

In this context, we may study the large time behavior of such solutions. In particular, we would like to know if, for large times, the solution behaves like the solution of the linear system. Such property is called (linear) scattering and has been extensively studied for Schrodinger equations or, more recently, for the Vlasov-Poisson system. However, fewer scattering results are known for the Vlasov-Maxwell system. In this talk, we will consider the solutions exhibited by Glassey and Strauss and exhibit a modified scattering dynamic. Moreover, we will show that, unless a non-generic condition is satisfied, we cannot recover a linear scattering property.