Regularity Bounds on Zakharov System Evolutions
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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)||Hs ≤ C|t|(s - 1)+, where Hs 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.
CitationColliander, J., & Staffilani, G. (2002). Regularity bounds on Zakharov system evolutions. Electronic Journal of Differential Equations, 2002(75), pp. 1-11.
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