Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Strichartz inequalities for fractional and higher order
  Schr\"odinger equations   We investigate a class of sharp Fourier extension inequalities on the planar
curves $s=|y|^p$, $p>1$. We identify the mechanism responsible for the possible
loss of compactness of nonnegative extremizing sequences, and prove that
extremizers exist if $1<p<p_0$, for some $p_0>4$. In particular, this resolves
the dichotomy of Jiang, Pausader & Shao concerning the existence of extremizers
for the Strichartz inequality for the fourth order Schr\"odinger equation in
one spatial dimension. One of our tools is a geometric comparison principle for
$n$-fold convolutions of certain singular measures in $\mathbb{R}^d$, developed
in a companion paper. We further show that any extremizer exhibits fast
$L^2$-decay in physical space, and so its Fourier transform can be extended to
an entire function on the whole complex plane. Finally, we investigate the
extent to which our methods apply to the case of the planar curves
$s=y|y|^{p-1}$, $p>1$.

26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex