Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global solutions for random vorticity equations perturbed by gradient
  dependent noise, in two and three dimensions   The aim of this work is to prove an existence and uniqueness result of
Kato-Fujita type for the Navier-Stokes equations, in vorticity form, in $2-D$
and $3-D$, perturbed by a gradient type multiplicative Gaussian noise (for
sufficiently small initial vorticity). These equations are considered in order
to model hydrodynamic turbulence. The approach was motivated by a recent result
by V. Barbu and the second named author in \cite{b1}, that treats the
stochastic $3D$-Navier-Stokes equations, in vorticity form, perturbed by linear
multiplicative Gaussian noise. More precisely, the equation is transformed to a
random nonlinear parabolic equation, as in \cite{b1}, but the transformation is
different and adapted to our gradient type noise. Then global unique existence
results are proved for the transformed equation, while for the original
stochastic Navier-Stokes equations, existence of a solution adapted to the
Brownian filtration is obtained up to some stopping time.

24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics