Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy concentration of the focusing energy-critical FNLS   We consider the fractional nonlinear Schr\"odinger equation (FNLS) with
general dispersion $|\nabla|^\alpha$ and focusing energy-critical
nonlinearities $-|u|^\frac{2\alpha}{d-\alpha}u$ and $-(|x|^{-2\alpha} * |u|^2)
u$. By adopting Kenig-Tsutsumi \cite{mets}, Kenig-Merle \cite{keme} and
Killip-Visan \cite{kv} arguments, we show the energy concentration of radial
solutions near the maximal existence time. For this purpose we use Sobolev
inequalities for radial functions and establish strong energy decoupling of
profiles. And we also show that when the kinetic energy is confined the maximal
existence time is finite for some large class of initial data satisfying the
initial energy $E(\varphi)$ is less than energy of ground state $E(W_\alpha)$
but $\||\nabla|^\frac\alpha2 \varphi\|_{L^2} \ge \||\nabla|^\frac\alpha2
W_\alpha\|_{L^2}$.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th