Regularity Bounds on Zakharov System Evolutions
arXiv:math/0203140
Abstract
Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution is shown to satisfy an estimate $\Hsup s {u(t)} \leq C {{|t|}^{(s-1)+}}$, where is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrödinger equation which reduces matters to bilinear estimates.
10 pages