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Published July 1996 | public
Journal Article

Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure

Abstract

We establish an existence result for the three‐dimensional MHD equations (∇ x B) x B = ∇p, ∇·B = 0, B·n|∂T = 0 with p ≠ const in tori T without symmetry. More precisely, our theorems insure the existence of sharp boundary solutions for tori whose departure from axisymmetry is sufficiently small; they allow for solutions to be constructed with an arbitrary number of pressure jumps.

Additional Information

© 1996 John Wiley & Sons, Inc. Received June 1995. We thank the anonymous reviewer for a number of useful suggestions. OB gratefully acknowledges stimulating conversations with P. Garabedian on nonaxisymmetric plasma equilibria; he also wishes to acknowledge support from NSF (through an NYI award and Grants Nos. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowship program), from the Powell Research Foundation, and from the AFOSR (contract no. F49620-96-1-0008). PL thanks Luigi Chierchia and Rafael de la Llave for valuable discussions concerning KAM theory.

Additional details

Created:
August 19, 2023
Modified:
October 19, 2023