Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations   We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD
for short) equations. The constructed weak solutions do not conserve the
magnetic helicity and can be close to any given smooth, divergence-free and
mean-free velocity and magnetic fields. Furthermore, we prove that the weak
solutions constructed by Beekie-Buckmaster-Vicol [2] for the ideal MHD can be
obtained as a strong vanishing viscosity and resistivity limit of a sequence of
weak solutions to MHD equations. This shows that, in contrast to the weak ideal
limits, Taylor's conjecture does not hold along the vanishing viscosity and
resistivity limits. Unlike in the context of the NSE [13] and the ideal MHD
[2], new types of velocity and magnetic flows, featuring both the refined
spatial and temporal intermittency, are constructed to respect the geometry of
MHD and to control the strong viscosity and resistivity. Compatible algebraic
structure is derived in the convex integration scheme. More interestingly, the
new intermittent flows indeed enable us to prove the aforementioned results for
the hyper-viscous and hyper-resistive MHD equations up to the sharp exponent
$5/4$, which coincides exactly with the Lions exponent for 3D hyper-viscous
NSE.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom