Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coercivity and stability results for an extended Navier-Stokes system   In this article we study a system of equations that is known to {\em extend}
Navier-Stokes dynamics in a well-posed manner to velocity fields that are not
necessarily divergence-free. Our aim is to contribute to an understanding of
the role of divergence and pressure in developing energy estimates capable of
controlling the nonlinear terms. We address questions of global existence and
stability in bounded domains with no-slip boundary conditions. Even in two
space dimensions, global existence is open in general, and remains so,
primarily due to the lack of a self-contained $L^2$ energy estimate. However,
through use of new $H^1$ coercivity estimates for the linear equations, we
establish a number of global existence and stability results, including results
for small divergence and a time-discrete scheme. We also prove global existence
in 2D for any initial data, provided sufficient divergence damping is included.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph