Regularity Bounds on Zakharov System Evolutions

2002/03/14 by J. Colliander, G. Staffilani, Colliander, J. +1
Mathematics · #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q55

paper · pdf · doi:10.48550/arxiv.math/0203140

10 pages

arxiv created 2002/03/14 · arxiv updated 2009/11/30

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) ≤ 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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