Scattering for the quartic generalised Korteweg-de Vries equation

Terence Tao

Scattering for the quartic generalised Korteweg-de Vries equation

偏微分方程分析 2007-05-23 v1

作者: Terence Tao

摘要

We show that the quartic generalised KdV equation $u_t + u_{xxx} + (u^4)_x = 0$ is globally wellposed for data in the critical (scale-invariant) space $\dot H^{-1/6}_x(\R)$ with small norm (and locally wellposed for large norm), improving a result of Gr\"unrock. As an application we obtain scattering results in $H^1_x(\R) \cap \dot H^{-1/6}_x(\R)$ for the radiation component of a perturbed soliton for this equation, improving the asymptotic stability results of Martel and Merle.

关键词

global well-posedness and scattering for nonlinear dispersive equations scattering theory nonlinear schrödinger equation

引用

@article{arxiv.math/0605357,
  title  = {Scattering for the quartic generalised Korteweg-de Vries equation},
  author = {Terence Tao},
  journal= {arXiv preprint arXiv:math/0605357},
  year   = {2007}
}

备注

28 pages, no figures, submitted, J. Diff. Eq

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