Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite dimensional reduction and convergence to equilibrium for
  incompressible Smectic-A liquid crystal flows   We consider a hydrodynamic system that models the Smectic-A liquid crystal
flow. The model consists of the Navier-Stokes equation for the fluid velocity
coupled with a fourth-order equation for the layer variable $\vp$, endowed with
periodic boundary conditions. We analyze the long-time behavior of the
solutions within the theory of infinite-dimensional dissipative dynamical
systems. We first prove that in 2D, the problem possesses a global attractor
$\mathcal{A}$ in certain phase space. Then we establish the existence of an
exponential attractor $\mathcal{M}$ which entails that the global attractor
$\mathcal{A}$ has finite fractal dimension. Moreover, we show that each
trajectory converges to a single equilibrium by means of a suitable
Lojasiewicz--Simon inequality. Corresponding results in 3D are also discussed.

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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
14
The categories of this paper are: math-ph