Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian and Godunov Structures of the Grad Hierarchy   The time evolution governed by the Boltzmann kinetic equation is compatible
with mechanics and thermodynamics. The former compatibility is mathematically
expressed in the Hamiltonian and Godunov structures, the latter in the
structure of gradient dynamics guaranteeing the growth of entropy and
consequently the approach to equilibrium. We carry all three structures to the
Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we
recognize the structures in the infinite Grad hierarchy and then in several
examples of finite hierarchies representing extended hydrodynamic equations. In
the context of Grad's hierarchies we also investigate relations between
Hamiltonian and Godunov structures.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci