Abstract
This survey presents our recent results in Morando et al. 2023, where we establish the local-in-time existence and the nonlinear stability of current-vortex sheets in ideal compressible Magnetohydrodynamics, provided a suitable stability condition is satisfied at each point of the initial discontinuity.
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Morando, A., Secchi, P., Trebeschi, P., Yuan, D. (2024). Local Existence of 2D Compressible Current-Vortex Sheets. In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume I. HYP 2022. SEMA SIMAI Springer Series, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-031-55260-1_24
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