Regularity Bounds on Zakharov System Evolutions

J. Colliander; G. Staffilani

Regularity Bounds on Zakharov System Evolutions

偏微分方程分析 2007-05-23 v1

作者: J. Colliander , G. Staffilani

摘要

Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution $u(t)$ is shown to satisfy an estimate $\Hsup s {u(t)} \leq C {{|t|}^{(s-1)+}}$ , where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schr\"odinger equation which reduces matters to bilinear estimates.

引用

@article{arxiv.math/0203140,
  title  = {Regularity Bounds on Zakharov System Evolutions},
  author = {J. Colliander and G. Staffilani},
  journal= {arXiv preprint arXiv:math/0203140},
  year   = {2007}
}

备注

10 pages

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