2013/11/25 by Alessandro Morando, Yuri Trakhinin, Morando, Alessandro +3 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Applied mathematics #Classification of discontinuities #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Magnetohydrodynamics #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Plasma #Quantum mechanics #math.AP
paper · pdf · doi:10.48550/arxiv.1311.6373
published in arXiv (Cornell University) (Cornell University) · 40 pages
openalex publication_date 2013/11/25 · arxiv created 2014/06/27 · arxiv updated 2014/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics (MHD). They are characteristic discontinuities with no flow across the discontinuity for which the pressure, the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump. Under the Rayleigh-Taylor sign condition [∂ p/∂ N]<0 on the jump of the normal derivative of the pressure satisfied at each point of the unperturbed contact discontinuity, we prove the well-posedness in Sobolev spaces of the linearized problem for 2D planar MHD flows.