Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Application of the Renormalization-group Method to the Reduction of
  Transport Equations   We first give a comprehensive review of the renormalization group method for
global and asymptotic analysis, putting an emphasis on the relevance to the
classical theory of envelopes and on the importance of the existence of
invariant manifolds of the dynamics under consideration. We clarify that an
essential point of the method is to convert the problem from solving
differential equations to obtaining suitable initial (or boundary)
conditions:The RG equation determines the slow motion of the would-be integral
constants in the unperturbative solution on the invariant manifold. The RG
method is applied to derive the Navier-Stokes equation from the Boltzmann
equation, as an example of the reduction of dynamics. We work out to obtain the
transport coefficients in terms of the one-body distribution function.

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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg