Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cauchy problem of the semilinear second order evolution equation
  with fractional Laplacian and damping   In the present paper, we prove time decay estimates of solutions in weighted
Sobolev spaces to the second order evolution equation with fractional Laplacian
and damping for data in Besov spaces. Our estimates generalize the estimates
obtained in the previous studies. The second aim of this article is to apply
these estimates to prove small data global well-posedness for the Cauchy
problem of the equation with power nonlinearities. Especially, the estimates
obtained in this paper enable us to treat more general conditions on the
nonlinearities and the spatial dimension than the results in the previous
studies.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin