Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat
  conducting Navier-Stokes and magnetohydrodynamic equations with vacuum at
  infinity   We revisit the 2D Cauchy problem of nonhomogeneous heat conducting
magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. For the initial density
allowing vacuum at infinity, we derive the global existence and uniqueness of
strong solutions provided that the initial density and the initial magnetic
decay not too slowly at infinity. In particular, the initial data can be
arbitrarily large. This improves our previous work where the initial density
has non-vacuum states at infinity. The result could also be viewed as an
extension of the study in L{\"u}-Xu-Zhong for the inhomogeneous case to the
full inhomogeneous situation. The method is based on delicate spatial weighted
estimates and the structural characteristic of the system under consideration.
As a byproduct, we get the global existence of strong solutions to the 2D
Cauchy problem for nonhomogeneous heat conducting Navier-Stokes equations with
vacuum at infinity.

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The categories of this paper are: cs
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph