Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the rigidity from infinity for nonlinear Alfv\'en waves   The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas and
the dynamics of Alfv\'en waves are governed by a system of nonlinear partial
differential equations called the MHD system. In this paper, we study the
rigidity aspect of the scattering problem for the MHD equations: We prove that
the Alfv\'en waves must vanish if their scattering fields vanish at infinities.
The proof is based on a careful study of the null structure and a family of
weighted energy estimates.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys