Well-Posedness of the Plasma–Vacuum Interface Problem for Ideal Incompressible MHD

• DOI: 10.1007/s00205-019-01386-5
• Publication Date: 2019-04-20T13:02:58Z
• Authors: Yongzhong Sun; Wei Wang; Zhifei Zhang
• Keywords: Interface (matter)

In this paper, we prove the local well-posedness of plasma-vacuum interface problem for ideal incompressible magnetohydrodynamics under the stability condition: the magnetic field $\mathbf{h}$ and the vacuum magnetic field $\hat{\mathbf{h}}$ are non-collinear on the interface(i.e., $|\mathbf{h}\times \hat{\mathbf{h}}|>0$), which was introduced by Trakhinin as a stability condition for the compressible plasma-vacuum interface problem.