Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Time Decay Estimates for the Landau Equation on Torus   We study the time decay estimates for the linearized Landau equation on torus
when the initial perturbation is not necessarily smooth. Our result reveals the
kinetic and fluid aspects of the equation. We design a Picard-type iteration
and Mixture lemma for constructing the increasingly regular kinetic like waves,
they are carried by transport equations and have exponential time decay rate.
The fluid like waves are constructed as part of the long-wave expansion in the
spectrum of the Fourier mode for the space variable and the time decay rate
depends on the size of the domain. The Mixture lemma plays an important role in
this paper, this lemma is parallel to Boltzmann equation but the proof is more
challenge.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th