Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant Gibbs measure and global strong solutions for the Hartree NLS
  equation in dimension three   In this paper we consider the defocusing Hartree nonlinear Schr\"odinger
equations on $\mathbb T^3$ with real valued and even potential $V$ and Fourier
multiplier decaying like $|k|^{-\beta}$. By relying on the method of random
averaging operators in arXiv:1910.08492, we show that there exists $\frac{1}{2}
\ll \beta_0 <1 $ such that for $ \beta > \beta_0 $ we have invariance of the
associated Gibbs measure and global existence of strong solutions in its
statistical ensemble. In this way we extend Bourgain's seminal result [7] which
requires $\beta >2$ in this case.

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The categories of this paper are: hep-ex
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci