Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic approach for homogeneous and non-homogeneous second order PDE's
  with an analytical solution of Navier Stokes Equations on $\mathbb{R}^3$ for
  a viscous incompressible fluid   Under this method second order \textbf{partial differential equations
(PDE's)} can be reduce to first order PDE's, simplifying the Initial value
problem \textbf{IVP} or Border value Problem \textbf{BVP} for most cases of
second-order differential equation, letting easiest proofs for existence and
uniqueness of the PVI and BVP problems.

9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con