Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Estimates for Generalized Forchheimer Flows of Slightly
  Compressible Fluids   This paper is focused on the generalized Forchheimer flows of slightly
compressible fluids in porous media. They are reformulated as a degenerate
parabolic equation for the pressure. The initial boundary value problem is
studied with time-dependent Dirichlet boundary data. The estimates up to the
boundary and for all time are derived for the $L^\infty$-norm of the pressure,
its gradient and time derivative. Large-time estimates are established to be
independent of the initial data. Particularly, thanks to the special structure
of the pressure's nonlinear equation, the global gradient estimates are
obtained in a relatively simple way, avoiding complicated calculations and a
prior requirement of H\"older estimates.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc