Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 75, pp. 1-11.
Title: Regularity bounds on Zakharov system evolutions
Authors: James Colliander (Univ. of Toronto, Canada)
Gigliola Staffilani (Massachusets Inst. of Technology, USA)
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
$\|u(t)\|_{H^s} \leq C |t|^{(s-1)+}$,
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.
Submitted March 15, 2002. Published August 20, 2002.
Math Subject Classifications: 35Q55
Key Words: initial value problems; bilinear estimates;
Zakharov system; weak turbulence.