Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Classical Solutions to the Relativistic Boltzmann Equation
  without Angular Cut-off   We prove the unique existence and exponential decay of global in time
classical solutions to the special relativistic Boltzmann equation without any
angular cut-off assumptions with initial perturbations in some weighted Sobolev
spaces. We consider perturbations of the relativistic Maxwellian equilibrium
states. We work in the case of a spatially periodic box. We consider the
general conditions on the collision kernel from Dudy\'nski and Ekiel-Je\'zewska
(Commun Math Phys \textbf{115}(4):607--629, 1985). Additionally, we prove sharp
constructive upper and coercive lower bounds for the linearized relativistic
Boltzmann collision operator in terms of a geometric fractional Sobolev norm;
this shows that a spectral gap exists and that this behavior is similar to that
of the non-relativistic case as shown by Gressman and Strain (Journal of AMS
\textbf{24}(3), 771--847, 2011). Lastly, we derive the relativistic analogue of
Carleman dual representation of Boltzmann collision operator. This is the first
global existence and stability result for relativistic Boltzmann equation
without angular cutoff and this resolves the open question of perturbative
global existence for the relativistic kinetic theory without the Grad's angular
cut-off assumption.

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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph