Well-posedness of the linearized problem for contact MHD discontinuities

2013/11/25 by Alessandro Morando, Yuri Trakhinin, Morando, Alessandro +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1311.6373

openalex publication_date 2013/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Well-posedness for the motion of an incompressible liquid with free surface boundary
• Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary condition

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