Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of nonnegative solutions to stochastic thin-film equations in
  two space dimensions   We prove the existence of martingale solutions to stochastic thin-film
equations in the physically relevant space dimension $d=2$. Conceptually, we
rely on a stochastic Faedo-Galerkin approach using tensor-product linear finite
elements in space. Augmenting the physical energy on the approximate level by a
curvature term weighted by positive powers of the spatial discretization
parameter $h$, we combine Ito's formula with inverse estimates and appropriate
stopping time arguments to derive stochastic counterparts of the energy and
entropy estimates known from the deterministic setting. In the limit $h\searrow
0$, we prove our strictly positive finite element solutions to converge towards
nonnegative martingale solutions -- making use of compactness arguments based
on Jakubowski's generalization of Skorokhod's theorem and subtle exhaustion
arguments to identify third-order spatial derivatives in the flux terms.

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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas