Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions of ideal MHD which do not conserve magnetic helicity   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.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph