Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost sure global well posedness for the radial nonlinear Schrodinger
  equation on the unit ball I: the 2D case   Our first purpose is to extend the results from \cite{T} on the radial
defocusing NLS on the disc in $\mathbb{R}^2$ to arbitrary smooth (defocusing)
nonlinearities and show the existence of a well-defined flow on the support of
the Gibbs measure (which is the natural extension of the classical flow for
smooth data). We follow a similar approach as in \cite{BB-1} exploiting certain
additional a priori space-time bounds that are provided by the invariance of
the Gibbs measure.
  Next, we consider the radial focusing equation with cubic nonlinearity (the
mass-subcritical case was studied in \cite{T2}) where the Gibbs measure is
subject to an $L^2$-norm restriction. A phase transition is established, of the
same nature as studied in the work of Lebowitz-Rose-Speer \cite{LRS} on the
torus. For sufficiently small $L^2$-norm, the Gibbs measure is absolutely
continuous with respect to the free measure, and moreover we have a
well-defined dynamics.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs