Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global exponential stability of classical solutions to the hydrodynamic
  model for semiconductors   In this paper, the global well-posedness and stability of classical solutions
to the multidimensional hydrodynamic model for semiconductors on the framework
of Besov space are considered. We weaken the regularity requirement of the
initial data, and improve some known results in Sobolev space. The local
existence of classical solutions to the Cauchy problem is obtained by the
regularized means and compactness argument. Using the high- and low- frequency
decomposition method, we prove the global exponential stability of classical
solutions (close to equilibrium). Furthermore, it is also shown that the
vorticity decays to zero exponentially in the 2D and 3D space. The main
analytic tools are the Littlewood-Paley decomposition and Bony's para-product
formula.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics