Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized final-state problem for the Zakharov system in dimension
  three   We consider the final-state problem for the Zakharov system in the energy
space in three space dimensions. For $(u_+, v_+) \in H^1 \times L^2$ without
any size restriction, symmetry assumption or additional angular regularity, we
perform a physical-space randomization on $u_+$ and an angular randomization on
$v_+$ yielding random final states $(u_+^\omega, v_+^\omega)$. We obtain that
for almost every $\omega$, there is a unique solution of the Zakharov system
scattering to the final state $(u_+^\omega, v_+^\omega)$. The key ingredient in
the proof is the use of time-weighted norms and generalized Strichartz
estimates which are accessible due to the randomization.

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
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph