Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near Sharp Strichartz estimates with loss in the presence of degenerate
  hyperbolic trapping   We consider an $n$-dimensional spherically symmetric, asymptotically
Euclidean manifold with two ends and a codimension 1 trapped set which is
degenerately hyperbolic. By separating variables and constructing a
semiclassical parametrix for a time scale polynomially beyond Ehrenfest time,
we show that solutions to the linear Schr\"odiner equation with initial
conditions localized on a spherical harmonic satisfy Strichartz estimates with
a loss depending only on the dimension $n$ and independent of the degeneracy.
The Strichartz estimates are sharp up to an arbitrary $\beta>0$ loss. This is
in contrast to \cite{ChWu-lsm}, where it is shown that solutions satisfy a
sharp local smoothing estimate with loss depending only on the degeneracy of
the trapped set, independent of the dimension.

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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: physics
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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: hep-th
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The categories of this paper are: econ