Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost sure global well-posedness for the energy supercritical
  Schr\"odinger equations   We consider the Schr\"odinger equations with arbitrary (large) power
non-linearity on the three-dimensional torus. We construct non-trivial
probability measures supported on Sobolev spaces and show that the equations
are globally well-posed on the supports of these measures, respectively.
Moreover, these measures are invariant under the flows that are constructed.
Therefore, the constructed solutions are recurrent in time.\\ Also, we show
\textit{slow growth} control on the time evolution of the solutions. A
generalization to any dimension is given. Our proof relies on a new approach
combining the fluctuation-dissipation method and some features of the Gibbs
measures theory for Hamiltonian PDEs. The strategy of the paper applies to
other contexts

33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics