Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dynamics above the ground state for the energy-critical
  Schrodinger equation with radial data   Consider the focusing energy critical Schrodinger equation in three space
dimensions with radial initial data in the energy space. We describe the global
dynamics of all the solutions of which the energy is at most slightly larger
than that of the ground states, according to whether it stays in a neighborhood
of them, blows up in finite time or scatters. In analogy with the paper by
Schlag and the first author on the subcritical equation, the proof uses an
analysis of the hyperbolic dynamics near them and the variational structure far
from them. The key step that allows to classify the solutions is the one-pass
lemma. The main difference from the subcritical case is that one has to
introduce a scaling parameter in order to describe the dynamics near them. One
has to take into account this parameter in the analysis around the ground
states by introducing some orthogonality conditions. One also has to take it
into account in the proof of the one-pass lemma by comparing the contribution
in the variational region and in the hyperbolic region.

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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con