Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernoulli's type Law of Euler Equations on Sobolev Space in
  $\mathbb{R}^{3}$   In this paper, we discuss Bernoulli's principle to the 3-dimensional
incompressible Euler equation in a bounded local Lipschitz domain
$\Omega\subset\mathbb{R}^{3}$ with a Lipschitz boundary. Using topological
properties of the level set and Morse-Sard theorem, we will prove Bernoulli's
principle on Sobolev space.

3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph