Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Scaling Exponents in Fluid Turbulence from First
  Principles: the Formal Setup   We propose a scheme for the calculation from the NS equations of the scaling
exponents $\zeta_n$ of the $n$th order correlators in fully developed
hydrodynamic turbulence. The scheme is nonperturbative and constructed to
respect the fundamental rescaling symmetry of the Euler equation. It
constitutes an infinite hierarchy of coupled equations that are obeyed
identically with respect to scaling for any set of $\zeta_n$. As a consequence
$\zeta_n$ are determined by solvability conditions and not from power counting.
It is arguedthat in order to achieve such a formulation one must recognize that
the many-point space-time correlators are not scale invariant in time
arguments. The assumption of full scale invariance leads unavoidably to K41
exponents. It is argued the determination of of $\zeta_n$ requires equations
for infinitely many renormalized objects. One ca n however proceed in
controlled successive approximations by truncations of the infinite hierarchy
of equations. Clues as to how to truncate without reintroducing power counting
can be obtained from renormalized perturbation theory. To this aim we show that
the fully resummed perturbation theory is equivalent in its contents to the
exact hierarchy of equations obeyed by the $n$th order correlators and Green's
function. In light of this important result we can safely use finite
resummations to construct successive closures. This paper presents the
conceptual and technical details of the scheme. The analysis of the high-order
closure procedures which do not destroy the rescaling symmetry and the actual
calculations for truncated models will be presented in a forthcoming paper in
collaboration with V. Belinicher.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph