We consider the free boundary problem for relativistic plasma-vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic Magneto-Hydrodynamics, while the vacuum magnetic and electric fields satisfy the Maxwell's equations. The plasma and vacuum magnetic fields remain tangential to the interface, which moves with the motion of the plasma. This yields a nonlinear multidimensional hyperbolic problem with a free boundary that is characteristic of variable multiplicity.

We establish a quantitative linear stability result for three-dimensional relativistic plasma-vacuum interfaces with variable coefficients.

Moreover, we prove the local-in-time existence and uniqueness of solutions to the nonlinear problem in two-dimensional space, provided that the plasma and vacuum magnetic fields do not vanish simultaneously at any point of the initial interface.

This is a joint work with Y. Trakhinin (Novosibirsk) and T. Wang (Wuhan).