Regularity Bounds on Zakharov System Evolutions

Details Regularity Bounds on Zakharov System Evolutions Regularity Bounds on Zakharov System Evolutions

2002-03-14

arxiv.org/abs/math/0203140v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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.

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