Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on endpoint Strichartz estimates for Schr\"odinger equations
  with the critical inverse-square potential   The purpose of this paper is to study the validity of global-in-time
Strichartz estimates for the Schr\"odinger equation on $\mathbb{R}^n$, $n\ge3$,
with the negative inverse-square potential $-\sigma|x|^{-2}$ in the critical
case $\sigma=(n-2)^2/4$. It turns out that the situation is different from the
subcritical case $\sigma<(n-2)^2/4$ in which the full range of Strichartz
estimates is known to be hold. More precisely, splitting the solution into the
radial and non-radial parts, we show that (i) the radial part satisfies a
weak-type endpoint estimate, which can be regarded as an extension to higher
dimensions of the endpoint Strichartz estimate with radial data for the
two-dimensional free Schr\"odinger equation; (ii) other endpoint estimates in
Lorentz spaces for the radial part fail in general; (iii) the non-radial part
satisfies the full range of Strichartz estimates.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat