Energy-supercritical NLS: critical $\dot H^s$-bounds imply scattering

Rowan Killip; Monica Visan

Energy-supercritical NLS: critical $\dot H^s$-bounds imply scattering

Analysis of PDEs 2008-12-12 v1

Authors: Rowan Killip , Monica Visan

Abstract

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.

Keywords

energy-supercritical nonlinear Schrödinger equation scattering critical Sobolev space a priori bounds

Cite

@article{arxiv.0812.2084,
  title  = {Energy-supercritical NLS: critical $\dot H^s$-bounds imply scattering},
  author = {Rowan Killip and Monica Visan},
  journal= {arXiv preprint arXiv:0812.2084},
  year   = {2008}
}

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