Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On one-dimension quasilinear wave equations with null conditions   In this paper, we show that one-dimension systems of quasilinear wave
equations with null conditions admit global classical solutions for small
initial data. This result extends Luli, Yang and Yu's seminal work [G. Luli, S.
Yang, P. Yu, On one-dimension semi-linear wave equations with null conditions,
Adv. Math.329 (2018) 174-188] from the semilinear case to the quasilinear case.
Furthermore, we also prove that the global solution is asymptotically free in
the energy sense. In order to achieve these goals, we will employ Luli, Yang
and Yu's weighted energy estimates with positive weights, introduce some
space-time weighted energy estimates and pay some special attentions to the
highest order energies, then use some suitable bootstrap process to close the
argument.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom