Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for weakly coupled systems of semi-linear structurally
  damped $\sigma$-evolution models with different power nonlinearities   In this paper, we study the Cauchy problems for weakly coupled systems of
semi-linear structurally damped $\sigma$-evolution models with different power
nonlinearities. By assuming additional $L^m$ regularity on the initial data,
with $m \in [1,2)$, we use $(L^m \cap L^2)- L^2$ and $L^2- L^2$ estimates for
solutions to the corresponding linear Cauchy problems to prove the global (in
time) existence of small data Sobolev solutions to the weakly coupled systems
of semi-linear models from suitable function spaces.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
18
The categories of this paper are: econ