Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior for 2D stochastic Navier-Stokes equations with
  memory in unbounded domains   We consider a stochastic model which describes the motion of a 2D
incompressible fluid in a unbounded domain with viscosity and memory effects.
This model is different from the classical stochastic Navier-Stokes-Voigt
equations due to the absence of the Voigt term $ -\alpha \Delta u_{t}$, and has
a much weaker dissipation than the usual Navier-Stokes-Voigt model since only
the memory viscoelasticity is present. We are interested in the global
well-posedness and long-time behaviors of this model. We first investigate the
well-posedness by using the classical Faedo-Galerkin method. Unlike the general
method of energy estimate, we then split the solution into two parts and get
the low-order and high-order uniform estimates, respectively. Based on the
uniform estimates of far-field values of solutions, we further prove the
existence and uniqueness of random attractors in unbounded domains with a
constructed compact subspace corresponding to memory. Finally, we give the
upper semicontinuity of the attractors when stochastic perturbation approaches
to zero.

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The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: econ
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: eess