Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kolmogorov's Theory of Turbulence and Inviscid Limit of the
  Navier-Stokes Equations in $\R^3$   We are concerned with the inviscid limit of the Navier-Stokes equations to
the Euler equations in $\R^3$. We first observe that a pathwise Kolmogorov
hypothesis implies the uniform boundedness of the $\alpha^{th}$-order
fractional derivative of the velocity for some $\alpha>0$ in the space
variables in $L^2$, which is independent of the viscosity $\mu>0$. Then it is
shown that this key observation yields the $L^2$-equicontinuity in the time and
the uniform bound in $L^q$, for some $q>2$, of the velocity independent of
$\mu>0$. These results lead to the strong convergence of solutions of the
Navier-Stokes equations to a solution of the Euler equations in $\R^3$. We also
consider passive scalars coupled to the incompressible Navier-Stokes equations
and, in this case, find the weak-star convergence for the passive scalars with
a limit in the form of a Young measure (pdf depending on space and time). Not
only do we offer a framework for mathematical existence theories, but also we
offer a framework for the interpretation of numerical solutions through the
identification of a function space in which convergence should take place, with
the bounds that are independent of $\mu>0$, that is in the high Reynolds number
limit.

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The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas