We consider the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics, where the Maxwell equations for electric and magnetic fields are considered in the vacuum region. Under a necessary and sufficient stability condition for a piecewise constant background state, we construct approximate solutions at any arbitrarily large order of accuracy to the free boundary problem in three space dimensions when the initial discontinuity displays high-frequency oscillations. Moreover, such approximate surface waves have nontrivial residual non-oscillatory components. The content of this chapter summarizes the result in Secchi and Yuan (Secchi P, Yuan Y (2022) Weakly nonlinear surface waves on the plasma–vacuum interface. J Math Pures Appl 163:132–203).
Geometric Optics for Surface Waves on the Plasma–Vacuum Interface: Higher Order Expansion
Paolo Secchi
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2024-01-01
Abstract
We consider the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics, where the Maxwell equations for electric and magnetic fields are considered in the vacuum region. Under a necessary and sufficient stability condition for a piecewise constant background state, we construct approximate solutions at any arbitrarily large order of accuracy to the free boundary problem in three space dimensions when the initial discontinuity displays high-frequency oscillations. Moreover, such approximate surface waves have nontrivial residual non-oscillatory components. The content of this chapter summarizes the result in Secchi and Yuan (Secchi P, Yuan Y (2022) Weakly nonlinear surface waves on the plasma–vacuum interface. J Math Pures Appl 163:132–203).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
