Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $L^{2}$ to $L^{\infty}$ approach for the Landau Equation   Consider the Landau equation with Coulomb potential in a periodic box. We
develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global
unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step
is to establish global $L^{2}$ estimates with strong velocity weight and time
decay, under the assumption of $L^{\infty }$ bound, which is further controlled
by such $L^{2}$ estimates via De Giorgi's method \cite{golse2016harnack} and
\cite{mouhot2015holder}. The second step is to employ estimates in $S_{p}$
spaces to control velocity derivatives to ensure uniqueness, which is based on
Holder estimates via De Giorgi's method \cite{golse2016harnack},
\cite{golse2015holder}, and \cite{mouhot2015holder}.

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The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga