TY - JOUR
T1 - Woltjer's variational principle, II
T2 - The case of unbounded domains
AU - Laurence, Peter
AU - Avellaneda, Marco
N1 - Funding Information:
This work was completed while P.L. was visiting the Institute for Advanced Study and he would like to thank the School of Mathematics and his host Luis Caffarelli in particular for making his stay very rewarding. Both authors would like to thank two anonymous referees and one of the editors, Andrew soward, for many helpful suggestions for improving the presentation of the material contained herein. This research was supported in part by US. Air Force grant AFOSR-90-0090, US. Army grant ARO-DAAL0389-KJ-0039 and National Science Foundation grant NSF-DMS-90-05799.
PY - 1993/6
Y1 - 1993/6
N2 - We show for a wide class of unbounded domains, that minimizing the magnetic energy subject to prescribed helicity or relative helicity, does not lead to nontrivial force-free fields. Instead, we show by an explicit construction that all minimizing sequences satisfying the helicity constraint, converge to a vacuum field.
AB - We show for a wide class of unbounded domains, that minimizing the magnetic energy subject to prescribed helicity or relative helicity, does not lead to nontrivial force-free fields. Instead, we show by an explicit construction that all minimizing sequences satisfying the helicity constraint, converge to a vacuum field.
KW - Helicity
KW - lack of compactness, energy
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U2 - 10.1080/03091929308203580
DO - 10.1080/03091929308203580
M3 - Article
AN - SCOPUS:0042634749
SN - 0309-1929
VL - 69
SP - 201
EP - 241
JO - Geophysical & Astrophysical Fluid Dynamics
JF - Geophysical & Astrophysical Fluid Dynamics
IS - 1-4
ER -