Regularity bounds on Zakharov system evolutions

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 $u(t)$ is shown to satisfy an estimate $|u(t)|_{H^s} leq C |t|^{(s-1)+}$, where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of ear...

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Bibliographic Details
Published in:Electronic journal of differential equations Vol. 2002; no. 75; pp. 1 - 11
Main Authors: James Colliander, Gigliola Staffilani
Format: Journal Article
Language:English
Published: Texas State University 01-08-2002
Subjects:
bilinear estimates
initial value problems
weak turbulence
Zakharov system
Online Access:Get full text
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Summary: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 $|u(t)|_{H^s} leq C |t|^{(s-1)+}$, where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrodinger equation which reduces matters to bilinear estimates.
ISSN:1072-6691