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Well-posedness for moving interfaces in anisotropic plasmas

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Abstract

We study the local-in-time well-posedness for an interface that separates an anisotropic plasma from a vacuum. The plasma flow is governed by the ideal Chew–Goldberger–Low (CGL) equations, which are the simplest collisionless fluid model with anisotropic pressure. The vacuum magnetic and electric fields are supposed to satisfy the pre-Maxwell equations. The plasma and vacuum magnetic fields are tangential to the interface. This represents a nonlinear hyperbolic-elliptic coupled problem with a characteristic free boundary. By a suitable symmetrization of the linearized CGL equations, we reduce the linearized free boundary problem to a problem analogous to that in isotropic magnetohydrodynamics (MHD). This enables us to prove the local existence and uniqueness of solutions to the nonlinear free boundary problem under the same non-collinearity condition for the plasma and vacuum magnetic fields on the initial interface required by Secchi and Trakhinin (Nonlinearity 27:105–169, 2014) in isotropic MHD.

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  1. Sobolev Institute of Mathematics, Koptyug Av. 4, Novosibirsk, Russia, 630090

    Yuri Trakhinin

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  1. Yuri Trakhinin
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Y.T wrote the main manuscript text and obtained all the results described in the work.

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Correspondence to Yuri Trakhinin.

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This research was carried out at the Sobolev Institute of Mathematics, under a state contract (Project No. FWNF-2022-0008).

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Trakhinin, Y. Well-posedness for moving interfaces in anisotropic plasmas. Z. Angew. Math. Phys. 74, 142 (2023). https://doi.org/10.1007/s00033-023-02035-4

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  • DOI: https://doi.org/10.1007/s00033-023-02035-4

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