Surface waves in the magnetopause: Regularity and time evolution

摘要

The equation describing surface waves in a one-dimensional magnetohydrodynamic discontinuity involves the Hilbert transform and is therefore nonlocal. It is found that by taking the analytic function whose real part is the first order perturbation one obtains a local equation. This equation yields several integral equalities which may be studied with the help of certain classical results of the theory of Hardy spaces. In particular this method provides information on the relation between the smoothness of the solution and its possible blow up in time.