Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three New Results on Continuation Criteria for the 3D Relativistic
  Vlasov-Maxwell System   In this paper, we consider sufficient conditions, called continuation
criteria, for global existence and uniqueness of classical solutions to the
three-dimensional relativistic Vlasov-Maxwell system. In the compact momentum
support setting, we prove that $\|p_{0}^{\frac{18}{5r} -
1+\beta}f\|_{L^{\infty}_{t}L^{r}_{x}L^{1}_{p}} \lesssim 1$, where $1\leq r \leq
2$ and $\beta >0$ is arbitrarily small, is a continuation criteria. The
previously best known continuation criteria in the compact setting is
$\|p_{0}^{\frac{4}{r} - 1+\beta}f\|_{L^{\infty}_{t}L^{r}_{x}L^{1}_{p}} \lesssim
1$, where $1\leq r < \infty$ and $\beta >0$ is arbitrarily small, is due to
work by Kunze. Thus, our continuation criteria is an improvement in the $1\leq
r \leq 2$ range. In addition, we consider also sufficient conditions for a
global existence result to the three-dimensional relativistic Vlasov-Maxwell
system without compact support in momentum space, building on previous work by
Luk-Strain. In their work, it was shown that
$\|p_{0}^{\theta}f\|_{L^{1}_{x}L^{1}_{p}} \lesssim 1$ is a continuation
criteria for the relativistic Vlasov-Maxwell system without compact support in
momentum space for $\theta > 5$. We improve this result to $\theta > 3$. We
also build on another result by Luk-Strain, in which the authors proved the
existence of a global classical solution in the compact momentum support
setting given the condition that there exists a two-dimensional plane on which
the momentum support of the particle density remains fixed. We prove
well-posedness even if the plane varies continuously in time.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an