Communications in Mathematical Sciences

Volume 12 (2014)

Number 6

Influence of vacuum electric field on the stability of a plasma-vacuum interface

Pages: 1065 – 1100



Nikita Mandrik (Novosibirsk State University, Novosibirsk, Russia)

Yuri Trakhinin (Sobolev Institute of Mathematics, Novosibirsk, Russia)


We study the free boundary problem for the plasma-vacuum interface in ideal com- pressible magnetohydrodynamics. Unlike the classical statement, when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. We show that a sufficiently large vacuum electric field can make the planar interface violently unstable. We find and analyze a sufficient condition on the vacuum electric field that precludes violent instabilities. Under the assumption that this condition is satisfied at each point of the unperturbed nonplanar plasma-vacuum interface, we prove the well-posedness of the linearized problem in anisotropic weighted Sobolev spaces.


ideal compressible magnetohydrodynamics, vacuum Maxwell equations, plasma-vacuum interface

2010 Mathematics Subject Classification

35L50, 35Q35, 35R35, 76E17, 76E25, 76W05

Full Text (PDF format)