| Autor: |
Cho, Yonggeun, Hwang, Gyeongha, Shim, Yong-Sun |
| Rok vydání: |
2015 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 $\||\nabla|^\frac\alpha2 \varphi\|_{L^2} \ge \||\nabla|^\frac\alpha2 W_\alpha\|_{L^2}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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