Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy estimates for weakly hyperbolic systems of the first order   For a class of weakly hyperbolic systems of the form D_t - A(t,x,D_x), where
A(t,x,D_x) is a first-order pseudodifferential operator whose principal symbol
degenerates like t^{l_*} at time t=0, for some integer l_* \geq 1,
well-posedness of the Cauchy problem is proved in an adapted scale of Sobolev
spaces. In addition, an upper bound for the loss of regularity that occurs when
passing from the Cauchy data to the solutions is established. In examples, this
upper bound turns out to be sharp.

27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol