Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the blow-up problem and new a priori estimates for the 3D Euler and
  the Navier-Stokes equations   We study blow-up rates and the blow-up profiles of possible asymptotically
self-similar singularities of the 3D Euler equations, where the sense of
convergence and self-similarity are considered in various sense. We extend much
further, in particular, the previous nonexistence results of
self-similar/asymptotically self-similar singularities obtained in
\cite{cha1,cha2}. Some implications the notions for the 3D Navier-Stokes
equations are also deduced. Generalization of the self-similar transforms is
also considered, and by appropriate choice of the transform we obtain new
\textit{a priori} estimates for the 3D Euler and the Navier-Stokes equations.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph