Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower regularity solutions of the biharmonic Schr\"odinger equation in a
  quarter plane   This paper deals with the initial-boundary value problem of the biharmonic
cubic nonlinear Schr\"odinger equation in a quarter plane with inhomogeneous
Dirichlet-Neumann boundary data. We prove local well-posedness in the low
regularity Sobolev spaces introducing Duhamel boundary forcing operator
associated to the linear equation to construct solutions on the whole line.
With this in hands, the energy and nonlinear estimates allow us to apply
Fourier restriction method, introduced by J. Bourgain, to get the main result
of the article. Additionally, adaptations of this approach for the biharmonic
cubic nonlinear Schr\"odinger equation on star graphs are also discussed.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph