Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity of Cost Functional and Optimal FeedbackControls for the
  Stochastic Navier Stokes Equation in2D   We show the continuity of a specific cost functional $J(\phi) = \mathbb{E}
\sup_{ t \in [0,T]}(\varphi(\mathcal{L}[t,u_\phi(t), \phi(t)]))$ of the SNSE in
2D on an open bounded nonperiodic domain $\mathcal{O}$ with respect to a
special set of feedback controls $\{\phi_n\}_{n \geq 0}$, where $\varphi(x)
=\log(1 + x)^{1-\epsilon}$ with $0 < \epsilon <1$.

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The categories of this paper are: atom-ph
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph