Mathematics – Analysis of PDEs

Scientific paper

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2008-12-11

Mathematics

Analysis of PDEs

Scientific paper

We consider two classes of defocusing energy-supercritical nonlinear

Schr\"odinger equations in dimensions $d\geq 5$. We prove that if the solution

$u$ is apriorily bounded in the critical Sobolev space, that is, $u\in

L_t^\infty \dot H^{s_c}_x$, then $u$ is global and scatters.

**Killip Rowan**

Physics – Mathematical Physics

Scientist

**Visan Monica**

Mathematics – Analysis of PDEs

Scientist

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