Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Exact, Time-dependent Analytical Solution for the Magnetic Field in
  the Inner Heliosheath   We derive an exact, time-dependent analytical magnetic field solution for the
inner heliosheath, which satisfies both the induction equation of ideal
magnetohydrodynamics in the limit of infinite electric conductivity and the
magnetic divergence constraint. To this end, we assume that the magnetic field
is frozen into a plasma flow resembling the characteristic interaction of the
solar wind with the local interstellar medium. Furthermore, we make use of the
ideal Ohm's law for the magnetic vector potential and the electric scalar
potential. By employing a suitable gauge condition that relates the potentials
and working with a characteristic coordinate representation, we thus obtain an
inhomogeneous first-order system of ordinary differential equations for the
magnetic vector potential. Then, using the general solution of this system, we
compute the magnetic field via the magnetic curl relation. Finally, we analyze
the well-posedness of the corresponding Dirichlet boundary value problem,
specify compatibility conditions for the boundary values, and outline the
implementation of boundary conditions.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math