Regularity Bounds on Zakharov System Evolutions
Abstract
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 s u(t) ≤ C |t|(s-1)+, where Hs 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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