Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering for the radial focusing INLS equation in higher dimensions   We consider the inhomogeneous nonlinear Schr\"odinger equation $$ i u_t
+\Delta u+|x|^{-b}|u|^\alpha u = 0, $$ where
$\frac{4-2b}{N}<\alpha<\frac{4-2b}{N-2}$ (when $N=2$,
$\frac{4-2b}{N}<\alpha<\infty$) and $0<b<\min\{N/3,1\}$. For a radial initial
data $u_0\in H^1(\mathbb{R}^N)$ under a certain smallness condition we prove
that the corresponding solution is global and scatters. The smallness condition
is related to the ground state solution of $-Q+\Delta Q+
|x|^{-b}|Q|^{\alpha}Q=0$ and the critical Sobolev index
$s_c=\frac{N}{2}-\frac{2-b}{\alpha}$. This is an extension of the recent work
\cite{paper2} by the same authors, where they consider the case $N=3$ and
$\alpha=2$. The proof is inspired by the concentration-compactness/rigidity
method developed by Kenig-Merle \cite{KENIG} to study
$H^1(\mathbb{R}^N)$-critical problem and also Holmer-Roudenko \cite{HOLROU} in
the case of $H^1(\mathbb{R}^N)$-subcritical equations.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci