Regularity bounds on Zakharov system evolutions

Electronic Journal of Differential Equations

关键词: initial value problems;    bilinear estimates;    Zakharov system;    weak turbulence.;   

DOI  :  

来源: DOAJ

【 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 $|u(t)|_{H^s} leq C |t|^{(s-1)+}$, where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrodinger equation which reduces matters to bilinear estimates.

【 授权许可】

Unknown