Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local and global strong solutions to the stochastic incompressible
  Navier-Stokes equations in critical Besov space   Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a
multiplicative white noise, we establish the local existence and uniqueness of
the strong solution when the initial data take values in the critical space
$\dot{B}_{p,r}^{\frac{d}{p}-1}(\mathbb{R}^d)$.
  The proof is based on the contraction mapping principle, stopping time and
stochastic estimates. Then we prove the global existence of strong solutions in
probability if the initial data are sufficiently small, which contain a class
of highly oscillating "large" data.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg