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Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure

Bruno, Oscar P. and Laurence, Peter (1996) Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure. Communications on Pure and Applied Mathematics, 49 (7). pp. 717-764. ISSN 0010-3640. doi:10.1002/(SICI)1097-0312(199607)49:7<717::AID-CPA3>3.0.CO;2-C.

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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.

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URLURL TypeDescription<717::AID-CPA3>3.0.CO;2-C DOIArticle
Bruno, Oscar P.0000-0001-8369-3014
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.
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Charles Lee Powell FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0008
Issue or Number:7
Record Number:CaltechAUTHORS:20181106-153720174
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Official Citation:Bruno, O. P. and Laurence, P. (1996), Existence of three‐dimensional toroidal MHD equilibria with nonconstant pressure. Comm. Pure Appl. Math., 49: 717-764. doi:10.1002/(SICI)1097-0312(199607)49:7<717::AID-CPA3>3.0.CO;2-C
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90682
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 19:34
Last Modified:16 Nov 2021 03:34

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