Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost sure local well-posedness for a derivative nonlinear wave
  equation   We study the derivative nonlinear wave equation \( - \partial_{tt} u + \Delta
u = |\nabla u|^2 \) on \( \mathbb{R}^{1+3} \). The deterministic theory is
determined by the Lorentz-critical regularity \( s_L = 2 \), and both local
well-posedness above \( s_L \) as well as ill-posedness below \( s_L \) are
known. In this paper, we show the local existence of solutions for randomized
initial data at the super-critical regularities \( s\geq 1.984\). In comparison
to the previous literature in random dispersive equations, the main difficulty
is the absence of a (probabilistic) nonlinear smoothing effect. To overcome
this, we introduce an adaptive and iterative decomposition of approximate
solutions into rough and smooth components. In addition, our argument relies on
refined Strichartz estimates, a paraproduct decomposition, and the truncation
method of de Bouard and Debussche.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ