Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the stochastic Strichartz estimates and the stochastic nonlinear
  Schr\"odinger equation on a compact riemannian manifold   We prove the existence and the uniqueness of a solution to the stochastic
NSLE on a two-dimensional compact riemannian manifold. Thus we generalize a
recent work by Burq, G\'erard and Tzvetkov in the deterministic setting, and a
series of papers by de Bouard and Debussche, who have examined similar
questions in the case of the flat euclidean space with random perturbation. We
prove the existence and the uniqueness of a local maximal solution to
stochastic nonlinear Schr\"odinger equations with multiplicative noise on a
compact d-dimensional riemannian manifold. Under more regularity on the noise,
we prove that the solution is global when the nonlinearity is of defocusing or
of focusing type, d=2 and the initial data belongs to the finite energy space.
Our proof is based on improved stochastic Strichartz inequalities.

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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph