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Existence of three‐dimensional toroidal MHD equilibria with nonconstant pressure
Author(s) -
Bruno Oscar P.,
Laurence Peter
Publication year - 1996
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199607)49:7<717::aid-cpa3>3.0.co;2-c
Subject(s) - magnetohydrodynamics , toroid , torus , mathematics , symmetry (geometry) , boundary (topology) , boundary value problem , mathematical analysis , mathematical physics , mechanics , classical mechanics , physics , geometry , plasma , quantum mechanics
We establish an existence result for the three‐dimensional MHD equations $$(\nabla\times {\bf B})\times {\bf B} = \nabla p$$ $$\nabla\cdot {\bf B} = 0$$ $${\bf B}\cdot n\mid_{\partial T} = 0$$ 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. © 1996 John Wiley & Sons, Inc.