Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularization by noise in one-dimensional continuity equation   A linear stochastic continuity equation with non-regular coefficients is
considered. We prove existence and uniqueness of strong solution, in the
probabilistic sense, to the Cauchy problem when the vector field has low
regularity, in which the classical DiPerna-Lions-Ambrosio theory of uniqueness
of distributional solutions does not apply. We solve partially the open problem
that is the case when the vector-field has random dependence. In addition, we
prove a stability result for the solutions.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph