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Regularity Bounds on Zakharov System Evolutions

J. Colliander·G. Staffilani
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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 $\Hsup s {u(t)} \leq C {{|t|}^{(s-1)+}}$, where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrödinger equation which reduces matters to bilinear estimates.

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J. Colliander, G. Staffilani. 2002-03-14. Regularity Bounds on Zakharov System Evolutions. https://arxiv.org/abs/math/0203140

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