Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of martingale solutions and large-time behavior for a
  stochastic mean curvature flow of graphs   We are concerned with a stochastic mean curvature flow of graphs over a
periodic domain of any space dimension. We establish existence of martingale
solutions which are strong in the PDE sense and study their large-time
behavior. Our analysis is based on a viscous approximation and new global
bounds, namely, an $L^{\infty}_{\omega,x,t}$ estimate for the gradient and an
$L^{2}_{\omega,x,t}$ bound for the Hessian. The proof makes essential use of
the delicate interplay between the deterministic mean curvature part and the
stochastic perturbation, which permits to show that certain gradient-dependent
energies are supermartingales. Our energy bounds in particular imply that
solutions become asymptotically spatially homogeneous and approach a Brownian
motion perturbed by a random constant.

10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc