Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The well-posedness, ill-posedness and non-uniform dependence on initial
  data for the Fornberg-Whitham equation in Besov spaces   In this paper, we first establish the local well-posedness (existence,
uniqueness and continuous dependence) for the Fornberg-Whitham equation in both
supercritical Besov spaces $B^s_{p,r},\ s>1+\frac{1}{p},\ 1\leq p,r\leq+\infty$
and critical Besov spaces $B^{1+\frac{1}{p}}_{p,1},\ 1\leq p<+\infty$, which
improves the previous work \cite{y2,ho,ht}. Then, we prove the solution is not
uniformly continuous dependence on the initial data in supercritical Besov
spaces $B^s_{p,r},\ s>1+\frac{1}{p},\ 1\leq p\leq+\infty,\ 1\leq r<+\infty$ and
critical Besov spaces $B^{1+\frac{1}{p}}_{p,1},\ 1\leq p<+\infty$. At last, we
show that the solution is ill-posed in $B^{\sigma}_{p,\infty}$ with
$\sigma>3+\frac{1}{p},\ 1\leq p\leq+\infty$.

3
The categories of this paper are: physics
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org