Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Yudovich solutions for the ideal MHD equations   In this paper, we address the problem of weak solutions of Yudovich type for
the inviscid MHD equations in two dimensions. The local-in-time existence and
uniqueness of these solutions sound to be hard to achieve due to some terms
involving Riesz transforms in the vorticity-current formulation. We shall prove
that the vortex patches with smooth boundary offer a suitable class of initial
data for which the problem can be solved. However this is only done under a
geometric constraint by assuming the boundary of the initial vorticity to be
frozen in a magnetic field line.
  We shall also discuss the stationary patches for the incompressible Euler
system $(E)$ and the MHD system. For example, we prove that a stationary simply
connected patch with rectifiable boundary for the system $(E)$ is necessarily
the characteristic function of a disc.

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The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th