Regularity Bounds on Zakharov System Evolutions

Date

2002-08-20

Authors

Colliander, James
Staffilani, Gigliola

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

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
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.

Description

Keywords

Initial value problems, Bilinear estimates, Zakharov system, Weak turbulence

Citation

Colliander, J., & Staffilani, G. (2002). Regularity bounds on Zakharov system evolutions. <i>Electronic Journal of Differential Equations, 2002</i>(75), pp. 1-11.

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Attribution 4.0 International

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