Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional SPDEs driven by spatially correlated noise: existence of the
  solution and smoothness of its density   In this paper we study a class of stochastic partial differential equations
in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven
by a Gaussian noise white in time and correlated in space. The differential
operator is a fractional derivative operator. We show the existence, uniqueness
and H\"{o}lder's regularity of the solution. Then by means of Malliavin
calculus, we prove that the law of the solution has a smooth density with
respect to the Lebesgue measure.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con