Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breakdown of regularity of scattering for mass-subcritical NLS   We study the scattering problem for the nonlinear Schr\"odinger equation
$i\partial_t u + \Delta u = |u|^p u$ on $\mathbb{R}^d$, $d\geq 1$, with a
mass-subcritical nonlinearity above the Strauss exponent. For this equation, it
is known that asymptotic completeness in $L^2$ with initial data in $\Sigma$
holds and the wave operator is well-defined on $\Sigma$. We show that there
exists $0<\beta<p$ such that the wave operator and the data-to-scattering-state
map do not admit extensions to maps $L^2\to L^2$ of class $C^{1+\beta}$ near
the origin. This constitutes a mild form of ill-posedness for the scattering
problem in the $L^2$ topology.

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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: math-ph