Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity

被引：43

作者：

Beekie, Rajendra ^{[1
]}

Buckmaster, Tristan ^{[2
]}

Vicol, Vlad ^{[1
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

ANNALS OF PDE | 2020年 / 6卷 / 01期

基金：

美国国家科学基金会;

关键词：

ENERGY-CONSERVATION; ONSAGERS CONJECTURE; EULER FLOWS; DISSIPATION; HYDRODYNAMICS; NONUNIQUENESS; RELAXATION; EQUATIONS;

D O I：

10.1007/s40818-020-0076-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist finite energy weak solutions to ideal MHD which cannot be attained in the infinite conductivity and zero viscosity limit. Our proof is based on a Nash-type convex integration scheme with intermittent building blocks adapted to the geometry of the MHD system.

引用

页数：40

共 60 条

[1]

Aluie H., 2009, Ph.D. thesis

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