Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3D Euler equations and ideal MHD mapped to regular systems: probing the
  finite-time blowup hypothesis   We prove by an explicit construction that solutions to incompressible 3D
Euler equations defined in the periodic cube can be mapped bijectively to a new
system of equations whose solutions are globally regular. We establish that the
usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a
solution to the 3D Euler system is equivalent to a condition on the
corresponding \emph{regular} solution of the new system. In the hypothetical
case of Euler finite-time singularity, we provide an explicit formula for the
blowup time in terms of the regular solution of the new system. The new system
is amenable to being integrated numerically using similar methods as in Euler
equations. We propose a method to simulate numerically the new regular system
and describe how to use this to draw robust and reliable conclusions on the
finite-time singularity problem of Euler equations, based on the conservation
of quantities directly related to energy and circulation. The method of mapping
to a regular system can be extended to any fluid equation that admits a
Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D
magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of
2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the
mapping, we provide a thorough comparison of the analytical solution versus the
numerical solution in the case of 1D inviscid Burgers equation.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas