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Regularity Bounds on Zakharov System Evolutions
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 Schr\"odinger equation which reduces matters to
bilinear estimates.Comment: 10 page