Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Euler equations in a critical case of the generalized Campanato
  space   In this paper we prove local in time well-posedness for the incompressible
Euler equations in $\Bbb R^n$ for the initial data in $\mathscr {L}^{ 1}_{
1(1)}(\mathbb {R}^{n}) $, which corresponds to a critical case of the
generalized Campanato spaces $ \mathscr {L}^{ s}_{ q(N)}(\mathbb {R}^{n})$. The
space is studied extensively in our companion paper\cite{trans}, and in the
critical case we have embeddings $ B^{1}_{\infty, 1} (\Bbb R^n) \hookrightarrow
\mathscr {L}^{ 1}_{ 1(1)}(\mathbb {R}^{n}) \hookrightarrow C^{0, 1} (\Bbb
R^n)$, where $B^{1}_{\infty, 1} (\Bbb R^n)$ and $ C^{0, 1} (\Bbb R^n)$ are the
Besov space and the Lipschitz space respectively. In particular $\mathscr {L}^{
1}_{ 1(1)}(\mathbb {R}^{n}) $ contains non-$C^1(\Bbb R^n)$ functions as well as
linearly growing functions at spatial infinity. We can also construct a class
of simple initial velocity belonging to $ \mathscr {L}^{ 1}_{ 1(1)}(\mathbb
{R}^{n})$, for which the solution to the Euler equations blows up in finite
time.

13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics