Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized Levi condition for weakly hyperbolic Cauchy problems with
  coefficients low regular in time and smooth in space   We consider the Cauchy problem for weakly hyperbolic $m$-th order partial
differential equations with coefficients low-regular in time and smooth in
space. It is well-known that in general one has to impose Levi conditions to
get $C^\infty$ or Gevrey well-posedness even if the coefficients are smooth. We
use moduli of continuity to describe the regularity of the coefficients with
respect to time, weight sequences for the characterization of their regularity
with respect to space and weight functions to define the solution spaces.
Furthermore, we propose a generalized Levi condition that models the influence
of multiple characteristics more freely. We establish sufficient conditions for
the well-posedness of the Cauchy problem, that link the Levi condition as well
as the modulus of continuity and the weight sequence of the coefficients to the
weight function of the solution space. Additionally, we obtain that the
influences of the Levi condition and the low regularity of coefficients on the
weight function of the solution space are independent of each other.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph