Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strictly hyperbolic Cauchy problems with coefficients low-regular in
  time and space   We consider the strictly hyperbolic Cauchy problem
  \begin{align*}
  &D_t^m u - \sum\limits_{j = 0}^{m-1} \sum\limits_{|\gamma|+j = m}
a_{m-j,\,\gamma}(t,\,x) D_x^\gamma D_t^j u = 0, \newline
  &D_t^{k-1}u(0,\,x) = g_k(x),\,k = 1,\,\ldots,\,m,
  \end{align*}
  for $(t,\,x) \in [0,\,T]\times \mathbb{R}^n$ with coefficients belonging to
the Zygmund class $C^s_\ast$ in $x$ and having a modulus of continuity below
Lipschitz in $t$. Imposing additional conditions to control oscillations, we
obtain a global (on $[0,\,T]$) $L^2$ energy estimate without loss of
derivatives for $s \geq \{1+\varepsilon,\,\frac{2m_0}{2-m_0}\}$, where $m_0$ is
linked to the modulus of continuity of the coefficients in time.

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The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ