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. https://resolver.caltech.edu/CaltechAUTHORS:20181106-153720174

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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.

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Article

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URL	URL Type	Description
https://doi.org/10.1002/(SICI)1097-0312(199607)49:7<717::AID-CPA3>3.0.CO;2-C	DOI	Article

ORCID:

Author	ORCID
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.

Funders:

Funding Agency	Grant Number
NSF	DMS-9200002
NSF	DMS-9523292
Alfred P. Sloan Foundation	UNSPECIFIED
Charles Lee Powell Foundation	UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)	F49620-96-1-0008

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DOI:

10.1002/(SICI)1097-0312(199607)49:7<717::AID-CPA3>3.0.CO;2-C

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CaltechAUTHORS:20181106-153720174

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20181106-153720174

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

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90682

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CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

07 Nov 2018 19:34

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16 Nov 2021 03:34

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